Lethem is a city in Guyana.
South towards Brazil
From the center of Lethem it is quite possible to walk as far as the border, once you have completed the Guyanese border requirements, it's a rather long way over to the Brazilian side, so asking the officials at the office to help you (explain you are looking for a ride) you can get over in somebody's car. Once on the other side you can carry on hitching from just after the Brazilian border post, the road is heading straight first for Bonfim (don't let anyone take you into Bonfim, tell them to drop you on the road to Boa Vista if that is you direction or you will regret the walk back), then for Boa Vista.
North towards Georgetown
From the center of Lethem you can also walk just far enough out to be away from houses, and on the road towards Georgetown. There is a 3 way junction linking roads from the bridge to Brazil, downtown, and the Georgetown road, just after that on the Georgetown road is a good spot. Remember if you are heading to Georgetown you are embarking on a long and fascinating trip. Bring cash, bring food, bring water...