The translation of "self". Herself = ela/si mesma, myself = mim mesmo(a). This link has some explanations for some languages including Portuguese! http://en.m.wikipedia.org/wiki/Reflexive_pronoun -- link for the portuguese: http://www.nativlang.com/po/qg_pronouns_reflexive.htm
It would have different meanings. "Ele mente para si mesmo" could mean that the person doesnt accept something, try to hide his own mistakes or doesnt accept his own shortcomings. (Ex: ele mente para si mesmo quando diz que não gosta dela - it means that he loves her but he just doesnt want to accept it, his own feelings, but everybody around him knows his real feelings). On the other hand, "ele mente por si mesmo" means that he does that according to his own dispostion, sometimes on purpose, or when he thinks he's misleading people, but actually he's not. Hope you got what i mean...
Normally, doing something "por si mesmo" is doing "by yourself". (no help needed)
I could say "eu faço isso por você", and it would mean "I do that in your place".
But there could be another meaning, harder to explain....
"Eu faço isso por você" - I do that because of you/for you
So, in this second case "mentir por si mesmo" would mean something like "lie to save himself".