[6510]

The to slow approach is fun. If you freeze and use a reasonable engine a bit string could represent which moves match the engine move. (lets call it block 1) The missing moves could be 3 bit numbers like 000 for second best engine move, 001 for 3rd, 010 for 4th, 011 for 5th, 100 for 6th best move, 101 for 7th, 110 for 8th and 111 for other moves. (block 2) The other moves are simply put like E4, E24 or NF3G5.(block 3)

[dmurray]

For optimum compression with this approach, you'd use an engine that generated the most likely moves (perhaps given the time control and the players' ratings, since Lichess stores those anyway), not the strongest moves. That might not look much like a regular chess engine.

[thegeomaster]

In that case decompression might use significant CPU time, the cost of which can offset the storage savings.