The Angels (Jered Weaver and a reliever) pitched a no-hitter earlier this year only to lose 1-0 to the Dodgers I think.
But it was only 8 innings. By rule definition, that does not count. I think the Orioles also had 3 pitchers combine for a complete game (9 innings) no hitter in a losing cause in 1967 but I'm not sure.
There have been 13 no hitters lost in extra innings (again not credited as no hitters). Two of those were perfect games.

There was one game in 1917 where both pitchers tossed 9 innings of no hit ball. One lost it in the 10 and gave up a couple of runs while the opposing pitcher completed his and got credited with a 10 inning no hitter.