Sleep Time & Trick Execution with Henry's Lizard?

Generally speaking, yes.

But wouldn’t that kill the sleep time?Also what is the best lube for that?

Thin lube will make your yoyo responsive and won’t kill the spintime, however you will have to apply it more often, then you would thick lube.

The only avaiable lube for me is Long Spin by YYF will that work?

I suppose long spin lube is thin lube? it will work but you have to apply more and more often as it’s not designed for responsive play. You can use 3 in 1 oil, baby oil, singer oil, or basically any general purpose lube just fine.
That is exactly the downside of having responsive yoyos, lube kills spin time, you have to compromise.