I wouldn't read too far into Lee's visit with Barkley. The Jets have been doing their due diligence in recent weeks attending workouts for Geno Smith and Ryan Nassib along with a host of others. New York is not expected to take a quarterback with their first round pick however, it is a real possibility later in the draft if they do not add another veteran through free agency.
There are some intriguing talents at UConn that are right up the Jets' ally. Namely, Sio Moore, who could help bolster the Jets' linebacking corp. Dane Brugler of NFLDraftScout has some additional information on Moore from the Shrine Game practice in January:
Moore entered the week as an underrated prospect, but he showed during practice sessions what most already knew: He's a pretty good football player. He was a versatile performer in college with good production as a hybrid linebacker for the Huskies, not looking out of place when asked to play in space against either the run or pass. Even in non-contact drills, Moore's competitive drive and explosive hitting ability were evident, and he will likely earn a top-100 grade from more than a few NFL teams.