I (nearly) played through all of the levels in V3. Most of then were quite fun, except for some long and repetitive ones (like "Path to Mahimah") and the two levels I would put in the category "fool the player" (namely "Puzzlin' Evidence" and "Nothing Gold Can Stay"). Apart from them:

My favourites are: Going down, Another funeral... (at least after simplifying the digger placement), Five for Fighting, Suspended Animation and the last three levels in Heinous.
Attached is a bunch of replays. Names like "S2L13" stand for "stage 2, level 13". Most of them should (hopefully) be rather close to the intended solutions. Those I believe are not (or have other interesting things going on) are mentioned below.
S1L1 - Lesson 1 - Block: Good blocker tutorial, but imo not trivial enough for the very first level. You have two hatches, lemmings will die when left alone and some traps are around...
S1L3 - It's A-Bashing: If you bash too low on the bottom right end, it's impossible to still solve the level. I don't know if that's a good thing to have in a tutorial level?
S1L11 - Send in the Lemmings: The ceiling route is trivial and uninteresting.
S1L23 - Workin' on a chain: Way too hard for Friendly. There is a 1-pixel gap in the vertical chain on the right, which can have annoying consequences. And I doubt my solution is intended...
S1L25 - Ice Cave: Boring - just dig down and then bash!
S1L26 - Lemming Overboard: In the rocks in the middle there is a 1-pixel gap that will trap the lemmings between it and the steel wall on the right. Depending on whether this is inteded, I would suggest to remove this gap or make it more visible. On the top platform at the right I noticed that you made it slightly thinner unter the rock. You did this probably to disallow digging down and then bashing along the platform. Right now it isn't a priori clear that this won't work, so maybe make the whole platform several pixels thinner?
S1L30 - Oh Lemming, where art thou?: I was slightly disappointed that there was no repeat for this level with a reduced skill set.
S2L6 - And the Long Shadows: No need to bash through any one-way-wall, cf. replay.
S2L12 - The Path to Mahimah: Way too long and not really intersting.
S2L17 - What's for dinner?: Not my type of level and more of a Friendly level.
S2L20 - The Six o'clock Rush: Good level, but too hard for Flapdoodle.
S2L22 - Hard to Port!: There is a backroute which is much harder than the intended solution, but doesn't need the blocker.
S2L28 - Loophole: My solution needs a Lemmini-only behaviour, which I consider a glitch.
S3L1 - The Icarus Agenda: At the bottom of the one-way-wall there is steel that goes way further than the graphics suggest. This had me placing the miner wrongly on my first try.
S3L5 - Eight Slippery Lemmings: How did changing the RR make the level easier? (OK, at least when considering only my solution, which is likely to be unintended)
S3L6 - Lemmings in Motion: The hardest level in MobiLems. Not yet solved (and neither the Lix version).
S3L7 - Going Down?: Have some spare skills...
S3L16 - Another Funeral...: The hidden steel makes the digger placement complicated.
S3L17 - Puzzlin' Evidence: No fan of this level - the solution is rather easy and uninteresting, but you never expect this to work.
S3L19 - It Takes Time to Build: Backrouted.
S3L24 - Road to Nowhere: 98% without the bomber possible.
S3L25 - Babylon Fading: Not yet solved. But this level seems the same as in V1. What have you changed?
S4L5 - Nothing Gold Can Stay: Not a fan of such levels, especially with what you did to the exit object.
S4L6 - Every Which Way But Loose: Backrouted.
S4L11 - Honey, I have shrunk the levels II: 100% possible.
S4L13 - Suspended Animation: 93% possible.
S4L21 - Eye of the Needle: The second builder has to be placed rather precisely. It would be easier if the exit platform would be 1 pixel lower or if the steel flag starts a few pixels higher.
S4L23 - Tres Hombres: The builder placement needs to be extremly precise. Is there no possibility to modify the level to allow for one or two pixels leeway?
S4L24 - Lemmings with the Golden Gun: 91% possible.
S4L26 - Passing Engagement: Backrouted