Trump has won the last 10 ranking finals he has played in.
Trump saw off John Higgins in his semi-final while Robertson edged past Mark Selby.
Heathcote, ranked 69 in the world, had threatened an upset in Milton Keynes. Judd Trump survives scare to beat Louis Heathcote in English Open
Lines’ son Oliver has also been forced to withdraw as a contact.
O’Sullivan was sporting pink nail varnish to raise awareness of breast cancer.
Irishman Doherty beat the seeded Robertson en route to progressing to stage two in Milton Keynes.
The Leicester cueman edged his opponent in a tight contest.
The 39-year-old Londoner reached a first ranking final since 2016.
The six-time world champion Sullivan was in action for the first time since he triumphed at the Crucible last month.
Daniel Wells and Gary Wilson have tested positive, with Elliot Slessor and David Lilley also pulling out after coming into contact with Wilson.