Looking into as much info as I can about lycans I could something that is interesting. I found that lycans when they change durring a full moon are stronger will a clear night compared to a cloudy night. If they get stronger with the moon light, then would they be hurt from the moonbeam spell, or would they get stronger?

Moonbeam does radiant damage, so unless they're immune to radiant they take damage. Additionally, it has this effect

A shapechanger makes its saving throw with disadvantage. If it fails, it also instantly reverts to its original form and can't assume a different form until it leaves the spell's light.

So, not only would a, let's say werewolf, take damage, it might also revert to it's original form.