Can a Lucio ult counter a McCree ult?

Solution 1:

Situation 1: McCree's lock-on delay for each player is increased proportional to the amount of effective health gained through Lucio's ult. Given that McCree is allowed to use his ult unhindered, you are correct in your assumption that Lucio's ult would do very little.

That said, the delay caused by Sound Barrier is likely to afford your team the time to either prevent him from going through with it or at least to find suitable cover.

Situation 2: It is exactly as you have said. In my experience, and as indicated by a player's account of his experience in this reddit post, increasing a player's effective health removes McCree's lock on effect; however, I am not sure if this resets the delay entirely or if it just increases the delay proportional to the health gained. Either way, it's worth investigation.

In short, Lucio's ult is very effective at countering Deadeye.