Do you mean Loan Protection Insurance? If so, I have never heard of a private lender asking for it, but hey, he who has the money makes the rules. If it is a lenders title policy or property insurance with the lender listed as the mortgagee, then these are standard.
As far as being worried about their ability to close ask them to present at least 3 recent settlement statements with the borrowers information redacted. That's the ultimate proof they fund deals.
Other questions I would want to know - other than fees.
1) How long have they been a private lender?
2) Are you funding these deals with your own cash or are you brokering the funds? If so, are you licensed?
3) If brokering - is it one lender per deal or pooled funds?
4) Where are payments to be sent?
5) Do they provide you with 1098's at year end?
6) What is their policy on construction draws?
7) What is the average time it takes them to close? What is the fastest they have been able to close a deal?
8) Have you ever foreclosed on someone?
9) Have you ever called a loan due before its maturity date? If so, why?
I could keep going on questions to ask, but I would hope you can take over from this list. I have seen too many times where investors are so eager to get money from a private lender (and of course from whomever throws out the lowest rate), that they forget to actually know who the lender is. You are married to your lender for the period of agreed upon time. That can either be good or bad.
On the flip side, I have seen several "private lenders" just throw money at a deal with out knowing who the borrower is. The warm and fuzzy feeling can go away very quickly at the first sign of a problem.
At the end of the day, you are probably less likely to be scammed by a private lender (local person), but instead deal with somebody who is chasing yield and is unprofessional, nervous, slow, and knows just enough to be dangerous.