Lucas claimed (in an interview published in Empire Magazine Issue #156 (June 2002) that he intended for the audience to be unaware whether Vader was telling the truth until they watched the third film.
Lucas claims he had the notion in mind from the start, but the idea
didn't appear until the second draft of Empire, and in the first there
is the contradictory appearance of a different father (a ghostly
presence like Kenobi). Lucas also wrestled with the idea of keeping
schtum on Luke's parentage until the end of the third film, but
eventually found the perfect moment. "I conceived it so that you would
not know if Vader was lying or telling the truth," Lucas said. "You
have to have an escape hatch for kids psychologically so they can deny
it."
Note also that Luke, in the film's official novelisation (published in 1980) has much the same concerns to begin with, that Vader might be lying. By the end of the book/film he's pretty much accepted that Vader is his father and is more concerned with why Ben didn't tell him.
Luke’s mind whirled with those words. Everything was finally beginning to coalesce in his brain. Or was it? He wondered if Vader were telling him the truth—if the training of Yoda, the teaching of saintly old Ben, his own strivings for good and his abhorrence of evil, if everything he had fought for were no more than a lie.
He didn’t want to believe Vader, tried convincing himself that it was Vader who lied to him — but somehow he could feel the truth in the Dark Lord’s words. But, if Darth Vader did speak the truth, why, he wondered, had Ben Kenobi lied to him? Why? His mind screamed louder than any wind the Dark Lord could ever summon against him.