Not sure Dooling can only be signed for $2.7m - haven't seen that, but have seen his cap hold is closer to $4m.
Let's assume talent wise BOS is willing to trade its 2013 1st round pick for Lee (likely around the 25th pick.) They would still have CHA 2nd round pick (probably comprable talent, but much cheaper than the 25th pick) and their own pick.
So what's the cost of getting Lee? Assume he wants MLE money, about $5m.
Williams, Moore, Dooling at $2.5m get you there. If Houston is OK using a roster spot on Dooling, you send the difference between $2.5m and the vet min. Williams and Moore are expendable talent (no cost.) So it costs you something like a late first round pick and $1m. Plus you have to spend the money on Lee. I think that's reasonable.
Danny has some leverage with Moorey too: he can work out a S&T with Dallas for Terry than MLE Lee. So I don't think he should pay too much, but he should also not mess around too long and lose Lee.
That would leave BAE for Wilcox, Steis, or another big, which they should be able to find an OK 2nd string guy with.