What is it that he lied to you? Is it really very serious? Did
you think about why he told you a lie? I dunno for your case lah.
But I know of people who tell lies...but white lies lah. I know
it's bad to tell lies...however, sometimes we can't avoid that.
Confused? Well, I have a friend, whose bf is quite
possessive...doesn't like her to go out with guys at all. But those
guy friends were her very close ex-schoolmates. She used to be
buddy with them. At first, she truthfully tell her bf about her
friends and that they go out for coffee, talk on the phone...her bf
not happy...quarrel with her. Made her very sad. She tried not to
see her guy friends anymore. But she kept in contact with them
through phone. Her bf also not happy when she told him she talked
on the phone with them. She felt sad and sandwiched. Those are her
good friends, and this is her beloved bf...hard to choose. So now,
when she talks to her guy friends on the phone, she will not tell
him anymore. If she goes out with her guy friends (not alone
lah...but a group of maybe 2 gals and one guy cos she dun want any
misunderstandings) She knows thay if she tells him, he'll quarrel
with her, but she dun wanna lose close friends...so once in a blue
moon, she go out with these friends on a gathering, she will tell
him about the gals who are going but 'left' out the fact that
certain guys are going. She feel that she is not lying (though
self-deceiving) cos she told truth mah...only, she didn't tell the
whole picture. In this way, she can avoid a quarrel with her bf and
keep in contact with her friends. Yes, this is bad to tell
lies...but she couldn't think of a better solution lor. We tried to
help her...but really dunno how to help her solve her
problem.
Anyway...I'm trying to say...if he told you a harmless lie, maybe
you should think about why...why he told you a lie? Isit he is
always like that? Even to other people he'll also tell lies? Maybe
he likes to tell lies...not only to you? Well...I dunno...but I
heard of people who just can't help but like to tell lies. Maybe
you can communicate with him. Unless he is two-timing you or did
something really serious...I think, a little white lie is harmless.
If becos of some harmless lies, you wanna give up this
relationship, you may regret next time.
Dun give up so easily...maybe you can try to help him kick that
habit. Maybe you can tell him how you really feel. Tell him that
you love him and wanna trust him...but trust needs to be earned and
if he tells you a lie, the trust is gone and hard to build
again...and if he keeps lying to you, one day, you'll not be able
to trust him anymore...not able to trust him enough to entrust him
with your heart. And you'll have to put that trust in another guy
who value your trust. 
Good luck.