One of my friends uses Skull Lair in his deck and he uses it no matter who's turn it is, can he do that?

he can activate the card itself on your turn as its a trap card but the effect can only be activated on his turn i believe

a trap effect resolve on he same turn is activated, unless stated otherwise, skull lair can be used on yuor opponent turn too

He can activate it during either players turn since it is Quick-like Effect.

btw train , Quick-like Effect doesn't have to be activated when card is activated(fliped)

Its a trap card so the effect is always a spell speed 2, therefore it can activate on anyone's turn