I have been surprised at the times when I hear that people lie when their partner is open to the truth without repercussion. It may be something that can happen again. Or it may have been a one time issue that will not repeat. I think you have to understand why he lied in the first place to decide if you can forgive him.
I think we all make mistakes and part of building a strong relationship is knowing when to forgive and when to realize things are too toxic.