I do not think Sela was being honest with Picard. If she told Picard Tasha Yar was still alive, he may have made more of an effort to find her.
Do we know that Tasha Yar was really executed on Romulus?
Within the main canon, there's no good reason to assume that she's alive, nor any good reason to assume that Commander Sela's story was untrue.
You may wish to note that while the stage direction from the original script for TNG: Redemption, Part I doesn't explicitly confirm the truth of her statement, it certainly doesn't leave much scope for her to be lying either.
SELA: One night... when I was four...she came to me, bundled me up and told me to stay quiet as we left the compound.
I realized she was taking me away... away from my home, away from my father... so I cried out.
For a brief moment, she cannot hold his eye. There are complex, ambivalent feelings warring in her. But she continues...
SELA: My father had offered her life. He had given her a home, given her a daughter. How did she repay him? With betrayal.
And then, looking at him again...
SELA: They executed her.
That all being said, the Romulans are known for their intricate, many-layered deceptions so it's at least possible that she's still alive. There also exists the potential that Sela/Yar may make an appearance in the new Trek Series given that the latest rumours are that it will be set slightly before the events of TNG.