OK - so I've looked into it and it seems that a club can always contribute $500,000 to a buyout, and that amount does not impact the team's cap.
However, with a first round pick, you can only offer a very limited contract - the standard rookie scale contract for their draft position, give or take 20% (it is standard procedure to sign all rookies to 120% of the scale value - Michael Heisley, of the Grizzlies, caused quite a stir last year when he offered only the scale salary to his two rookies, which led to their agents holding them out of training camp, until the Grizzlies caved and offered the full 120%).
Anyway, this means that obviously the team cannot give a first round pick any money beyond their standard pay.
With 2nd round picks and undrafted players (or any free agent, such as Anthony Parker or Jorge Garbajosa before they came to the Raptors) the team can offer any contract size to that player, up to the maximum amount for their NBA experience. As such, although the team can only really pay $500,000 directly towards the buyout, they can reimburse the player throughout the first year of their contract with a much higher salary than they would usually get. Note that any part of the player's salary intended to go towards their buyout is still their salary - so it counts against the cap.
That Lithuanian league end date is interesting - so Valanciunas' cap hold will be back on the cap close to the start of the playoffs, so if Colangelo wants to use that part of the cap to absorb a player through a trade it will have to be in the first week of playoffs or so (depending on any lockout-caused schedule changes), or before the trade deadline, and he won't be able to use that cap space at the draft either.