Someone beat me to it, but I finished typing it and also included information about L2/L3, so I'm going to post it anyway.
Original game skills:
Climber, Floater, Blocker, Bomber, Builder, Basher, Miner, Digger.
Rule 1 must use this set; Rule 2 must avoid this set.
Original sets:
Dirt, Pillar, Marble, Crystal, Fire
Oh No sets are also allowed by rule 1:
Brick, Bubble, Rock, Snow
L2 and L3 sets are banned for both Rule 1 and Rule 2. These are:
Beach, Classic, Egyptian, Shadow, Sports, Outdoor, Medieval, Polar, Space, Cavelem, Circus, Highland, Biolab
No vertical scrolling is a bit vague since this can be dependent on zoom settings, but I assume these means keep the default height of 160 pixels, even though many (most?) screens will accept a slightly larger vertical size.
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Apparently this contest is near-entirely NeoLemmix only, though Lix does have some L1 inspired sets. It may be a good idea to allow just enough object usage in Lix to create a valid level (i.e. one entrance, one exit), as these concessions for Lix would allow 2 of the 3 rules to be possible in that engine, while the third rule just can't really be made to work in Lix in any meaningful way.