Lospalos is in East Timor.
Buses leave daily from Dili. Last known times (June 2013) were 2am and 2pm. More may leave but you will need to travel to the bus station/terminal and ask. Costs $7. Journey time is approximately 7 to 9 hours depending on conditions. There are at least two 20 minute breaks where you can buy food and use the toilet.
Buses from Baucau leave erratically depending on when the Dili buses departed (they must drive through Baucau). Simply wait at the roundabout outside the Posada Hotel and wave down a bus when it arrives. Costs $4, journey times approximately 3 to 5 hours depending on conditions.
By car or motorbike
Road conditions remained stable as of June 2013, and the drive was easy, as it is the main road heading east out of Dili and Baucau.
Roberto Carlos Hotel
Buses leave for Dili/Baucau in the evening starting from about 5pm and then hourly until 8pm. There are some that leave much earlier (1am) but you should speak to locals to understand when. Costs approximately $7, journey times are 8 hours to Dili and 4 for Baucau. Be aware that you may need to book a seat on a bus as they are popular, you should also get on the bus as far in advance as possible. If you don't then you may lose your booked seat or not even get on the bus!