is being investigated for allegedly threatening to burn down the house of a record label honcho who was in talks to work with his daughter Ali Lohan
As TMZ first reported, Lindsay's little sister is trying to make a go of it as a country music singer
... with a little help from her father Michael, of course.
According to sources, Michael brokered a potential deal between Chinga Chang Records and Ali ... securing a $15,000 consulting fee for himself too. We're told when Ali got wind that Michael was cashing in on her she freaked on him.
We're told Michael tried to nix the deal with Chinga Chang (say that five times fast), and eventually got into a threatening war of words with its CEO, Dan Herman.
Law enforcement sources tell us Lohan placed calls and texts to Herman ... claiming to know his Florida home is not well-secured, and would be easy to burn down.
Herman filed a report with the State Police in Pennsylvania, where he lives ... and cops tell us they are investigating.
Michael tells TMZ ... Herman is lying about the threats, and also about having a deal with Ali.