Johnson worked under his father at Yeovil, but moved to Hearts in January.
He failed to make an impact at Tynecastle, playing just twice as the Jambos secured the runners-up spot last season.
And Johnson senior inists his son is not guaranteed a place in the side.
"Lee will be treated the same as any other player at the club and will have to fight for his place in the team just like everybody else," he declared.
"At the end of the day it wasn't me who made the first steps towards bringing Lee here, it was the chairman who persuaded him to come."