* Lawmakers meet far from Tripoli, in eastern seaside town * Britain follows other Western nations and pulls diplomats * Fighting still raging at Tripoli airport By Patrick Markey and Aziz El Yaakoubi TRIPOLI, Aug 4 (Reuters) - Libya's newly elected parliament held its first formal session on Monday as rival armed factions continued to battle for dominance of a country that was a dictatorship for decades before Muammar Gaddafi's fall three years ago. Lawmakers gathered in a heavily guarded hotel in the eastern city of Tobruk after three weeks of fighting in Tripoli and in Benghazi had made the capital and the country's second city unsafe for the parliament session. Elected in June, the House of Representatives replaces the General National Congress (GNC) where, some analysts say, Islamist factions had more influence than in the new one.