We're trying to validate legal professionals as a segment via AdWords for our app that synchronises document viewing across multiple iPads. (no need for projector or hanging over shoulders, it also works remotely via VoIP).
The only AdWords keywords that will perform well on search are ones that directly describe your product, e.g. "document syncing." To target a segment like legal professionals, use AdWords' Contextual Targeting Tool to build ad groups to target websites that your target market would visit, e.g. anything related to law.
The ratio of people seeking legal services to professionals providing those services is many-to-one. If it weren't so, lawyers would have to charge their annual income for a single consultation.
What this means for you is that the vast majority of legal-keyword searches will be moving the wrong direction -- from layperson toward lawyers.
If you spend your money on those keywords, you'll be wasting your advertising budget attracting the exact opposite of legal professionals.
If you'd like advice on which specific keywords phrases to target, you'll find yourself paying someone due to the time required to gather appropriate data. SEM agencies exist for this reason. You're also welcome to give me a call for recommendations or to outsource some of the keyword research. No day goes by when I don't research such questions, albeit from a different angle.
Adwords is not the best platform when you want to target an "audience" instead of search terms. I would suggest you to use Facebook - targeting lawyers - or may be display ads - targeting pages visited by lawyers - and call out your app details in the ad copy. This will make sure that the persons clicking on the ad are from your target audience and are interested in what you have to offer.
Paid search can only capture people who are looking for an app.... which is usually less than 3%. In general 3% of your target audience is looking to buy what you are selling.
A better use of adwords would be to use the display network, running banner advertisements that promote your app ONLY on sites that lawyers visit for industry news. In that case there are no keywords, its what sites does your audience visit regularly. I'd be happy to explain this more on the phone.