In American English, we would say: "I was trying to find my lawyer but I heard that he's on vacation" Additionally, native speakers often substitute the verb "find" for "get a hold of" if you were trying to contact him through the phone or through email. "Find" gives the impression that you are physically searching for him

It's correct. While Americans often use the past simple in place of the present perfect, it's certainly not wrong to use the pp in this context in AmE. And in many other Englishes, the pp would be the more likely choice.

It's not wrong but it could be better. I'd say "I was looking for my lawyer but learned that he's on vacation."

Is lawyer just one expression in American English?

It's almost perfect. Try using '..., but I heard that he is on vacation'.