Does a relief pitcher who loses the lead then regains it get a win?

Rule 9.17(a) states:

The Official Scorer shall credit as the winning pitcher that pitcher whose team assumes a lead while such pitcher is in the game, or during the inning on offense in which such pitcher is removed from the game, and does not relinquish such lead

[ some exceptions which don't apply here ]

The relief pitcher in your example meets that definition, so they are the winning pitcher. What you're finding here is that wins and losses for pitchers aren't a very good measure of very much at all.

As an aside, as the relief pitcher entered the game in what was a save situation (a lead of no more than 3 runs) and failed to keep the lead, they would be "credited" with a blown save in this example. However, saves are probably an even less meaningful statistic than wins and losses.