The piece properties dialog is fairly similar to the one from the regular Lemmix editor, just with some additions. The first thing you might notice is that every option appears disabled in this screenshot - that's simply because they're only enabled when a relevant piece is selected.

Like with the Level Properties dialog, some options are exclusive to certain engines.

Terrain Options
The top-left section has options for terrain pieces. The top input box allows you to enter a piece ID number, while the "..." next to it pops up a dialog with images of every piece which you can select a piece from.

The "Erase" option causes the piece to act as an eraser instead of adding to the terrain layout. This option is available in all engines.
The "No Overwrite" option causes the piece to be drawn behind earlier pieces instead of in front of it. This option is available in all engines.
The "Invisible" option causes the piece to be invisible, but still functional. This option is only available in SuperLemmini.
The "Invert" option causes the piece to be drawn upside-down. This option is available in all engines.
The "Flip" option causes the piece to be flipped horizontally. This option is only available in NeoLemmix and SuperLemmini.
The "Fake" option causes the piece to be drawn, but not actually act as solid. This option is only available in SuperLemmini.
The "One-Way" option means the terrain piece can have one-way arrows applied to it. This option is only available in NeoLemmix and SuperLemmini; in other engines all terrain pieces may have one-way arrows applied to them.

Note that if the "One-Way Invert" option is selected in Level Properties; the "One-Way" option here works in reverse - one-way arrows can be applied only to pieces that don't have this option set.

Object Options
The bottom-left section has options for objects. Like with terrain, the top input box allows you to select a piece ID number, while the "..." next to it pops up a dialog with images of every object which you can select one from.

The "Only On Terrain" option causes the piece to only be drawn where it is overlapping a terrain piece. In NeoLemmix, it will only be drawn on terrain pieces with the One-Way option set (or not set, in the case of One-Way Invert being used); in all others, it will be drawn on any terrain - and in some, even on other objects.
The "Invert" and "Flip" options work the same way as for terrain; the same exclusivity (ie: Invert is in all engines, but Flip is only in NeoLemmix and SuperLemmini) also applies. The Flip option also moves the object's trigger area; the Invert option does so only in NeoLemmix (but SuperLemmini has a seperate option to move the trigger area as if the object were upside down and the two can be set independantly).
The "No Overwrite" option also functions the same way as it does for terrain pieces. An object with No Overwrite set will be drawn behind terrain as well as behind earlier objects.
The "Invert Trigger" option, which is SuperLemmini-exclusive, moves the object's trigger area as if the object were upside down. It is possible in SuperLemmini to set an object to display upside down but keep its trigger area in the normal place, or vice versa, due to these two options being seperate.
The "Face Left" option, which is only for NeoLemmix and SuperLemmini, causes a window to spawn left-facing lemmings, or a pre-placed lemming to initially face left. It can also be used on a splitter (in NeoLemmix) to make the first lemming that encounters it go left; whereas the default is for the first lemming to go right, or on a teleporter to invert the direction the lemming is facing when it comes out.
The "Fake" option causes the object to be drawn, but not function. This option is exclusive to NeoLemmix and SuperLemmini; though traditional Lemmix will treat all objects as fake if their index is 16 or higher.
The "Invisible" option is the inverse of "Fake"; it will cause the object to function, but not be drawn. This option is also exclusive to NeoLemmix and SuperLemmini. If both of these are set, the object will neither be drawn or functional.

The "S Value" and "L Value", which are NeoLemmix-exclusive, set specific properties on certian types of objects. The S Value can range from 0 to 15, while the L value can range from 0 to 255. (These originally stood for "Skill value" and "Level value", based on their function on the first types of object that used them, but could perhaps be better remembered as "Small value" and "Large value".)
Window - The L value determines what permanent skills the lemmings will spawn with. 1 = Climber, 2 = Swimmer, 4 = Floater, 8 = Glider, 16 = Mechanic, 64 = Zombie. These can be combined by adding the numbers together; and Zombie will only function if the level has the Zombie gimmick enabled. The S value does nothing.
Pre-Placed Lemming - The same as with Window, with one additional value that can be used; 32 = Blocker.
Pickup Skill - The S value determines which skill is used. The dropdown box to the right can also be used to quickly select a skill rather than having to know the values. In order from 0 to 15, the values correspond to Climber, Floater, Bomber, Blocker, Builder, Basher, Miner, Digger, Walker, Swimmer, Glider, Mechanic, Stoner, Platformer, Stacker, Cloner.
Secret Level Trigger - The S value determines the rank of the secret level, while the L value determines the level number. Setting the rank to 0 results in the current rank, while setting the level to 0 results in the first level in the target rank that's designated as a secret level.
Teleporter / Receiver / Two-Way Teleporter - These will only link to corresponding objects with the same S value.

Steel Options
There is only one option which is exclusive to steel, which is the type of steel area. In regular Lemmix / Lemmini levels, this option is not available. In SuperLemmini, only "Steel" or "Negative Steel" are allowed (the latter cancels out steel areas instead of adding them). In NeoLemmix, steel areas can also be used to make one-way walls (provided the graphic set in question has one-way-wall objects); however it should be noted that one-way walls made this way will not animate, so they should only be used if the graphic set's one-way arrows don't animate anyway (eg: Sega style, Cheapo-converted styles).

** The screenshot above just shows a "Negative Steel" checkbox instead of a multiple-selection menu; this is simply because it's a very old screenshot.

Steel areas can also have their size modified, but the width and height inputs are under the global options. There are limitations on what the size can be in some engines:

Lemmix - Both width and height must be divisible by 4, and can only be in the range of 4 to 64.
NeoLemmix - With and height can only be in the range of 1 to 256.
Lemmini - No limitations.
SuperLemmini - No limitations.

Global Options
The Left, Top, Width, Height and Index options apply to all piece types. The Left and Top are its coordinates (X and Y respectively). The Width and Height are the size of the piece; these are read-only except for steel areas where they can be modified. The index determines the ordering of pieces when drawing - higher-index ones will draw over / erase / etc lower-index ones (but the No Overwrite flag can alter this).

Index must be unique for each piece of the same type, and there are additional limitations on them depending on engine:

Lemmix
Terrain - Must be in the range 0 to 399
Object - Must be in the range 0 to 31; objects with an index 16 or higher are visible but do not function (except windows)
Steel - Must be in the range 0 to 31

NeoLemmix
Terrain - Must be in the range 0 to 999
Object - Must be in the range 0 to 127
Steel - Must be in the range 0 to 127

Lemmini and SuperLemmini
There are no restrictions on how high the index number can go, but unlike in Lemmix and NeoLemmix, there cannot be gaps in the saved level (there may be gaps while working on the level in the editor). NeoLemmix Editor will automatically shift pieces backwards to fill in any gaps if nessecary, so you do not need to worry about making an effort to avoid them; just don't rely on them remaining there.