I personally wouldn't ever say that (native speaker from the US). If you are trying to express that you always tell the truth, the most common way to explain this would be to say "I don't TELL lies."

A native speaker probably would very naturally say "I don't do lies." It's perhaps not the best English, but is perfect for sounding like a native. I'd personally say this, depending on the situation. For instance, I wouldn't say it at a job interview, but to my friends I would.

You could say "I don't do lies" but it is more natural to say I don't lie, I don't like lying... Hope this helps :)