Should we make sure our lawyer is not also working for competitors/acquirers?

I believe that in all states, working for competitive companies producing competitive products, would be a conflict of interest. The legal Bars of each state usually frown upon such activity with dire consequences for the attorney or firm, although it may be possible if both companies sign waivers, just so that all parties involved are aware of the "playing field" and what is transpiring in the "playing field".

How much do you trust attorney-client privilege? Also what are your data-sanitation policies? For example, if the lawyer is your patent agent, then they are already privy to future products but if they are just doing generic contracts, you may be able to blur key diagrams or expressly put "under legal privilege" on certain information. I don't know your industry but to be frank, most commercial (as opposed to deep technical) information has a short life-span so unless you are really in stealth mode with world-changing outcomes, I suspect you are worrying too much about competition and not enough about customers.

One business manager (think it was a Japanese firm?) once said the best business advantage is where you can invite in competitors to visit and benchmark, and they still can't duplicate (strengths in market distribution, internal culture, etc).