Training puzzle 11492 - missed better solution

the third White move in the solution is BxQ, however, checking first is even better (3.Qd8+ ... 4.BxQ).
Unfortunattly, this move is regarded as a mistake.

I can't check whether you are right on the one above, but the trainers on lichess are not in the best shape. I can bring some examples by my own experince on the opening trainer- I have seen there some puzzles that regarded wrong theory moves (in my own opening) as not "best", but real bad as the better ones instead. I can't find the example above (there it was a piece sacrifice that is the only way to hold the position) but here is another one
http://de.lichess.org/training/opening/2558
the only real theory moves are e5 and Be2. The solution is a4 instead of e5, but I have to admit, playing the same position as black against players ~2500 I have never ever heard or thought about move a4 (I think Bb7 is a nice counter for example). But nevertheless, the point is, the trainers are not unseless at all (decent for a free site), but far from perfect

The opening trainer is downright horrid. As for the training puzzles, the only bad thing is that you will fail the puzzle if you make a move that gives you +12 instead of a +13 position at the end of a long line. For example, in the puzzle given, playing Qd8+ is a +13.78 adv. at 25/45 depth and Bxg4 is a +14.69.

OP should also be less obvious when using an engine in his standard games, I lol'd at the fact a 1400 didnt get caught yet, but as the IM says, it's good enough for a free site.