Per Chris Kwan's thought, I agree. LOI's are merely conversational, and they get thrown around WAY too much by investors and entrepreneurs alike. LOI's are not binding as Chris alluded to. Not saying they are bad, but they hold next to no value as is, more or less a starting point.
If the investment firm has some cache, no doubt there is some value there to build on. If this investment firm is saying they will invest AFTER you close a low 7 figure deal, they sound like they are not willing to take any risk IN you. But I'm guessing they will want the reward of equity FROM you. How does that make you feel?
If the account you are to close pays upfront, why not just use that for your needed operating capital? One thing is for certain, if you do the heavy lifting before the P/E invests, you are going to have far more bargaining power.
It sounds like you are close. If you can hold out from investors a little longer. Be careful of LOI's though. They can really throw entrepreneurs off track. I would request a detailed terms sheet before I spent much more time with this investor. But that's just me.
Good news it sounds like you are close to having far more options than one investor.