The Judge is a transcended being that determines if a species is worthy of transcendence or if they should be annihilated, and then passes down their fate depending on the test subject's success or failure

Clarke was now a part of the test and she wasn’t prepared for memories of her dead girlfriend Lexa to be brought up.

Sometime later, long enough for Clarke to be annoyed by the Judge's absence, the Judge reappears as Lexa, knowing that Lexa was Clarke's greatest love.

Clarke runs over and hugs the Judge to which the Judge responds I’m not her, Clarke. Clarke brokenly says I know

The Judge however not only had access to Lexa’s form but her memories as well, but to be fair the Judge had access to everyone’s memories including Lexa.