What should we put in a co-founder contract and do we need a lawyer for it?

You've answered your own question by asking it. Firstly, let me say it is heartening to see that a group of people working on a project have the sense to reduce their arraignment to writing. All too often people come to me in the position of not having so done. Believe me, it will be much easier on all of you to have something in writing now. That being said, since you've ask what should be in your agreement, the answer is yes: you should have an attorney assist you with the drafting. You don't know and the lawyer will. It's not your business to know; that's what we're here for. I will not go into all the details of what should be in your agreement here. I will let whatever lawyer you hire do that. In your case, I tell clients to discuss amongst themselves what their deal should be. Then I come in and advise them on any terms they haven't thought of that are customary. I also counsel them on the investing and tax advantages of certain types of organization. Very important to get these things correct. Good luck.

There are a number of basics:
- weighting of each founders contribution - translating into shares, including a portion for future employees
- shareholder's agreement, how founders dispose, resolving voting conflicts (though can default in articles of association) or acquire from each other
- vesting schedule = expected timeframe for sweat equity to value in startup
- good/bad leaver provisions - what happens if for one reason or another a co-founder leaves (death, health, personal reasons)
There are a number of clauses relating to specific events like dispute resolution or liquidation but these are generally standardised in the various seed documents like Y-combinator or Techstar documents. Whilst a lawyer is useful to explain some of the more exotic terms like liquidity prefs, there are incubators and often entrepreneur friendly groups like Founders Institute who often have experienced mentors who've gone through the pain and can tell you why those clauses exist.