Both of their first solo songs can be interpreted to be breakup songs about the band. "Never Forget You" in particular seems to carry the message of "let it go already, tATu is dead."
10 years after the peak of their success, gay rights in Russia has gotten to the point where "propaganda" (basically, mentioning not being straight in a public environment) is illegal. Essentiallly, their efforts failed.
Their 2014 split looks almost exactly like a relationship breakup. First Lena posts a video out wanting nothing to do with Julia, then Julia replies with one about "sorting out their differences". The "Love in Every Moment" video highlights this unintentionally by them being in different rooms by Lena's choice, and Julia hugging it out with a Fake Shemp of Lena.