Not exactly time travel, but the protagonist changes multiple future realities with his dreams. It’s got cheap sets, no-name actors, the cheesiest 70s music score ever, mind control, a mad scientist AND aliens.
The Lathe of Heaven is a 1980 film adaptation of the 1971 science fiction novel The Lathe of Heaven by Ursula K. Le Guin. It was produced in 1979 as part of New York City public television station WNET's Experimental TV Lab project.
In Portland, Oregon, in the near future, George Orr is charged with misuse of prescription medications. He volunteers for psychiatric care to avoid prosecution, and is assigned to the care of licensed oneirologist William Haber. Orr has known since age 17 that his dreams change reality, and tries to prevent himself from dreaming because he fears their effects.
Haber initially considers Orr's fear as a delusional symptom of neurosis or psychosis. He puts Orr into a hypnotic trance, and encourages him to have an "effective dream" to record his brain function.
When he realizes Orr is telling the truth, Haber begins to use Orr's "effective dreams" to first create a prestigious, well-funded institute run by himself, then to attempt to solve various social problems.
Only after numerous failed attempts to "make the world right", Haber admits to Orr he believes in Orr's power. Having analyzed Orr's supremely complex dreaming brainwaves, Haber begins creating a machine that will similarly enhance his own and allow him to remake reality directly.
Orr turns to lawyer Heather LeLache for help in getting out of his government-mandated treatments with Haber. LeLache doubts Orr's sanity, but agrees to help him, eventually becoming an ally.