Each party should have representation before signing the agreement. The question that you need to ask yourself is when you want to get the second the lawyer involved. For example, your partner may want to go to his lawyer, tell him the agreement, have the document drafted and then you may want to take the draft to your lawyer to go over it and make sure that is corresponds with your intentions and adequately protects your rights.
It sounds like you want a cohabitation agreement and well as wills and possibly estate documents.
As the other response noted, you could each have your own representation, where one of you hires a lawyer to do the drafting and the other hires a lawyer to review it to make sure it's fair and what you''ve agreed to. Another option is to hire a lawyer jointly and waive any conlifct from them representing both of you.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.