It depends on what your plans for the property are. 

I am drafting the lease and planning to take it with me to closing, where we will be executing the document.

We had planned on eventually redoing the kitchens and floors in both units once we turned over new tenants, but the evictions accelerated that process.

Legitimate, in this case, means that the entity is part of an overall business investment strategy whereby you have a business plan, tax returns, and the funds you seek are for further business expansion.If, however, the LLC is a stand alone entity, is not profitable, or is not legitimate, then your probably better off putting into your personal name and securing funding that way, or still talking to local or regional banks to see if they have any loan programs available where you might be able to secure financing.

Do you plan to live there forever?

When I let people back in, had a detailed plan as people salvaged thru. 

Finally, check with the Town to make sure there are no municipal liens, Make sure they're on Town sewer, check with the tax assessor to see how many bedrooms the tax office thinks there are, (important if you are flipping) buy ok to have more bedrooms if you are planning to buy and hold.  

To simplify the existing lease I thought about asking the tenant if they would be ok modifying the addendums to get rid of the resident benefit package and the building protection plan. 

It requires careful planning and diligent execution.

You are going to get conflicting responses on this because a lot of it comes down to your plans and your tolerance for risk, which are things known only to you.