It has been a long time since I did it, but I don't remember there being any cooldown on doing the emotes.
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Tested today, Lurker summoned, everything works normally.
Confirmed; on our second attempt we had the Atlatean Gown wearing toon with us and were able to spawn The Lurker - and I can't remember that we did anything different than the last time...
Well, now we can concentrate to correctly kite/kill the initial brain-mobs... kiting wasn't the biggest problem - that was the initial random one-shot if they weren't irritated fast enough and ofc the random channelling veins from the red one which kept wiping us :-/
p.s. but at least we killed Infinity a few times \o/