I think "I need to look for a lawyer" is more accurate, find works be 找到
Came here to point this
一位律师、一名律师 are more suitable since lawyers are professionals and these are respected.
how about 我需要找一个（名/位）律师. I feel like 需要 shows "need" better because 要 alone could be interpreted as a statement of desire or future intent (rather than need) along the lines of "I want to find a lawyer" or "I am going to find a lawyer."
Yes, I prefer your translation as well.