Britain were seeded number two for the draw, ranked fifth out of 15 teams, following their debut performance at EuroBasket last year in Poland, when they lost all three games but turned in some impressive displays in a very tough group.
They will now face their four opponents both home and away, needing to finish either first in the group or as one of the two best second-placed teams in order to book their trip to Lithuania.
Should they fail, they would be entered with the nine other runners-up into the Additional Qualification/Relegation Round, in which one final place is on offer.
The games will be played throughout the month of August.
Finch (pictured) said: "We may have been seeded in the second pot for the draw but that didn't mean we took anything for granted.
"Make no mistake Division A is tough and perhaps last time we took people by surprise because we were a relatively unknown quantity, but now, we have been exposed to more top-level European basketball.
"Last year everyone said we were drawn in the group of death at the Europeans and yes, it was tough, but particularly against Spain we stepped up and raised our game.
"And that's what we will have to do this summer.
"With everyone available and the ability to prepare for this campaign correctly, I see no reason why we can't be one of the main contenders for qualifying."
Britain need to get to the 2011 EuroBasket as they aim to prove to world governing body FIBA they are ready to take up the hosts' place in London in 2012.
Britain's women, who face far longer odds of making the EuroBasket in Poland, will play the Slovak Republic, Ukraine and Germany in their qualifiers.
The women's team were seeded four for the draw, ranked 16th out of 18 teams, and will make survival at the Division A level their first priority.
Head coach Tom Maher said: "At this level every team is tough, that is the nature of the competition.
"Britain played six of the 18 teams in the draw in the last round of qualifying so we know what to expect.
"Slovak Republic, Ukraine and Germany will provide us with stiff opposition but I am encouraged by how the group of players I had last summer got on, both in training in Manchester and then at the World University Games, where we surprised a few people.
"I'm confident that with another good camp this year, and a fully fit roster available, we will be in a good position to challenge these three/four countries, and that's exactly what we need to do to stay on track for London 2012."
January 2010: Finch predicts London 2012 will help basketball explode in Britain
December 2009: Britain not given wild-card to World Championships
December 2009: Finch waiting for two big decisions
November 2009: Sir Steve leads calls for Britain's basketball team to be given wild-card
September 2009: Britain hoping for wild card invite to 2010 World Championships