Now when you say "lump" are you referring to an individual image or a collection of them between markers?
A lump is an entry in a WAD file. Each image is its own separate lump with its own lump name.
Furthermore, I renamed my images as you suggested and even gave the whole thing a free mapthingnumber, but there's another identifier if I'm not mistaking; a thingnumber? I don't have a clue as to what this is or how to use it.
There is no attribute called "thingnumber". Let's start from scratch:
The enemy you're making is an
Object (SOCEdit labels it a "Thing", but SOCEdit is wrong). The first and foremost attribute of an Object is its
Object number (or ID or whathaveyou), which is the Object
slot you're putting it in. For example, slot #1 contains MT_BLUECRAWLA, the Object for the blue Crawla. Slot #318 is the first freeslot. Presumably you're putting your custom enemy there, or in a different freeslot. The
MapThingNum is the number that is used when you put your Object on your map as a
Thing. A Thing is any Object that is placed directly on a map. It's a different number from the Object number. Some Objects don't even have a MapThingNum because they're not supposed to be placed directly on maps. Your enemy obviously needs one, so give it any Thing number that isn't in use, e.g. 122.
The
sprites are the images that your enemy display. The terminology on this isn't really clear, but let's call the whole set of images that you made for your enemy a "sprite". This sprite is divided into
frames, which are "still images" of sorts. The enemy cycles through these frames to create an animation. Each frame consists of up to eight "rotation" images, so that the sprite can be displayed from eight different angles. Now the lump names are as follows: "Fxxxyz". "xxx" is the number of the freeslot that the sprite should be in. For the first freeslot, choose "001". "y" is the frame, the first being "A", the second "B" and so forth. "z" is the rotation number. 1 is front, 3 is facing left, 5 is back, 7 is facing right and everything else is diagonal in-between. More on this can be found in the
Character WAD Tutorial, where you probably didn't look (and one can hardly blame you).
To set which part of the sprite is displayed at what point, you need to reference them in the Object's
states. States are essentially the "animation frames" of the Object. They define what the Object does and what frame it uses in a given moment of its animation cycle. (This is a bit tricky because I'm using the word "frame" both in relation to sprites and to states. It's not the same, I hope you understand what I mean.) For starters, it will suffice to make the enemy spawn and stand still the whole time. To do that, make a new state (use the next available freeslot for states). Set the sprite to "243 - SPR_F001 (Free slot)", the frame to 0 (this makes it display "F001Az"), tics to whatever you want except "0" and "-1" (for now the duration of the state is irrelevant because it loops back to itself), and make "next state" loop back to itself. Leave everything else empty. In the Object menu ("Edit Things" in SOCEdit), set the "SpawnState" to the new state you just created. Now your enemy should spawn and display its sprite properly. Of course it isn't animated yet.
The Wiki could use some Finer detail on custom enemies.
The wiki's documentation on all SOC stuff is very incomplete and incoherent. This topic is much more complex than mapping due to all the terminology involved and because SOC is simply a godawful mess to begin with.