A friend of mine gave me an LG L34C OPTIMUS FUEL, unfortunately it is locked with a pattern lock and she can't remember it. Is there a way to still factory reset the phone and if so, how do I do it?
No. If it were that easy, stealing phones would make sense. The registered owner (your friend, probably) has to bring it to the carrier it was registered with (or a good repair shop) with photo ID proving that it's hers, and they can remove the lock.
We don't give out that information here, because it would help people to steal phones.