Does X compare to the Beatles? That question shows who the Beatles are, whatever their merits as musicians, innovators, or cultural icons. What is the intention of the question? To know the relevance of either? To troll? To judge the musical abilities of one or the other? Where Lady Gaga stands in relation is something only time will tell, as has been mentioned. The Beatles are a band of many decades standing and their work continues after them far beyond the shores where they began and inspire many. Whether Lady Gaga has or will reach that level, I'd hope she would be happy to be aware of it and willing to help others with the level of fame and have wisdom to know when that was possible and humility to understand and be able to step back when it isn't.
Actually, the original question was:
I remember Beatlemania circa 1964 through 1970. Do you think Lady Gaga has achieved a similar level of international pop culture stardom?
The questions about her merits as a musician, her influence on music, and her place in history have been raised by other people--not the OP.
It's perfectly possible for artists to be wildly popular in their heyday, and then disappear without a trace. I'm sure all of us could list any number of one-hit wonders from our youth. Where are the
Snows of yesteryear?
And who today remembers the great musical stars of the distant past? The castrati singers of the 18th century, like Farinelli, whose arias are beyond the ability of most human beings to sing? The virtuoso performers of the 19th century, like Paganini and Liszt, who made women scream and swoon, just like the Beatles?
The only reason even classical-music fans remember composers from these eras is because they had the advantage of writing stuff down on paper. The people who performed their music are mostly forgotten. And the fact that we still remember the Beatles today has a lot more to do with the historical circumstances in which they performed and recorded than with any intrinsic merit in their music.