Lender may have a different view, but realistically - there's not a big risk of shock in the living room or in the bedrooms.
The problem with 2 wire outlets is this: If you end up with a short someone could get electrocuted. The 3 wire came about so excess electricity could pass harmlessly to ground through the third wire. Is there an actual ground wire going from the house into a stake driven into the ground? Maybe that is what he wants to see.
Talk to your town code enforcement officer. Ask him what the house needs to be legal. If he is ok with it then you may be able to show that in writing to the inspector. Did you get the electricians reply in writing? Show it to the inspector also. At that point you may get the same response, you may get a different one.
One last thing, a house that old could easily have lead paint and asbestos in it. Be sure to have it tested for those if you choose this place. Good luck.