Without a Jewish mother they are not Jewish at all & are as Jewish as you,Karol Wojtyla,Josef Ratzinger or Jorge Bergoglio!!
That's my point. Actual Jews don't describe themselves as lost.
For Gentiles pretending to be Jewish, see these guys for example:
"They also believe in Two House theology, which makes a distinction between the Tribe of Judah and the Ten Lost Tribes, and that ultimately, European people represent the Ten Lost Tribes."
https://en.wikipedia.org/wiki/Christian_Identity