I don't think that's true. You can have a good relationship and not have to lie about anything.
My boyfriend and I always talked about other people that we found attractive. I think it's healthy in a relationship to be able to talk about who you think is attractive. He told me he looked at p 0 r n and told me that he spank the monkeyd at least once a day and sometimes more. It's no big deal because I knew that yes, he was pleasuring himself without me but it's not like he was going to other people to do it. You just have to accept that him looking at p 0 r n or going to hooters is not going to stop. Learn to accept it and deal with it and he will stop lying.
As long as you know that your boyfriend loves you then you should be able to accept that yes, he is going to look at other women, but it is just looking.