In his controversial new documentary, “Lover of Men” filmmaker Shaun Peterson makes a compelling case for the theory that President Abraham Lincoln was gay.

We caught up with the director on “TMZ Live” Friday, where Peterson touched on some of the evidence presented in the doc … including 2 instances where the 16th President of the United States shared a bed with close male friends for extended periods of time.

Peterson notes it was a common practice for men to share a bed in those days, as a way to save money … but Lincoln did not face financial restraints at the time, earning several incomes from being a legislator and lawyer — yet he still chose to split a mattress with businessman Joshua Fry Speed for 4 years.

Peterson understands this theory is a tough one for some who revere the famous president to accept. But he says the evidence backs his bold claim … and invites his critics — including Elon Musk, Alex Jones and Ben Shapiro — to sit down with him and watch the doc in its entirety.

He’s positive they’d see his side of the debate, especially if they keep an open mind and listen to the facts.

Though we think Peterson will be waiting 4 score and 7 years before Musk, Jones and Shapiro sign off on his theory!!!