I reckon the difficulties you sound like you're facing in lithunwrap are actually purely because of the toolset available and the clunky interface in lithunwrap - not cos of any inability on your part. I used lith for years not knowing any better, and yeah UV mapping was perpetually a HORRIBLE process and got more and more horrible as my shapes got more complex.
Eventually Water pointed out to me that Blender actually had a very good UV mapping suite built in. I took a bit of convincing to give it a solid go (simply cos until that point I had ONLY used blender for mesh construction), but once I did I completely abandoned Lith. Blender's tools are both easier to use than Liths AND far more flexible. UV mapping is now very easy, but can still be a bit time consuming depending on just how pedantic I want to be (which is usually... quite :\ ).
The process consists of:
1) Selecting the face or faces to UV using whatever selection tools you like (as in tools like: select all linked faces, select all linked co-planar faces with an angle tolerance, select all similar to current selection (based on size, direction etc) - and a few other neat tools like increment selection which adds all faces touching the currently selected faces to the selection)
2a) Pressing unwrap to auto-unwrap it's UVs. You might need to select some key edges and mark them as seams to get it to unwrap correctly.
OR
2b) Orientating the camera so it's facing the selected faces straight on (there's a tool to quickly and precisely do that too), project the selected faces from the current view onto the UV plane.
3) Scale and arrange the UV 'islands' to maximise texture space usage. (there are tools to do this automatically too!)
Not saying you SHOULD switch to blender (though....you still should!

) but the point is that other apps do exist that have much better toolsets than lith and ESPECIALLY TS. (I don't think I'd even count TS as having a UV toolset. It more has a lone rusty bent screwdriver made of cheese, and pretends it's a full on CNC machining workshop.)