May an IRA make a loan to an LLC which is managed by the IRA owner and which is owned 49% by the IRA owner and 51% by an unrelated party?

No.

This is a prohibited transaction unde Code Section 4975

It is not necessarily a pt.

Based on the stated facts, the LLC is not a "disqualified person" with respect to the IRA. Therefore, it is not a per se pt.

It would be a pt only if it is considered (I'm sort of paraphrasing) an act by the IRA owner whereby he deals with the income or assets of the IRA in his own interest or for his own account. In other words, it has to be a "self-dealing" type of transaction, which is determined by the facts and circumstances.

Without knowing any of the facts and circumstances, my guess is that it's probably not a good idea for the IRA owner to do this. trougd : one that is intended to benefit the IRA owner in some capacity

Sounds an awful like self dealing to me, which would make me suspicious about all transactions. Legal? Don't know, let the accountants respond. Lots of custodians would prohibit the investment simply because of the year end valuation issue.

One reason you may NOT want to do a transaction like this is that you lose the normal tax write-off if the business has a loss or fails completely. You did not describe the entity... but if it was a high risk start-up, that could be an issue.