We caught up with the talk show host in the Big Apple Friday and asked him all about his upcoming interview with Elon ... he's challenging people to sit down, watch the interview and let him know why he's not the right voice for X -- 'cause Don says he can't figure it out!

Lemon -- who says he's open to speaking to Musk despite his recent firing -- says he's giving the platform the kind of conversation he thinks it needs ... and he wants X to hire people with his viewpoint to further its free speech goals.

When asked if he'd consider the Shannon Sharpe/"Club Shay Shay" route -- DL seems to be thinking about it, and he's got nothing but praise for the former Denver Bronco.

As for whether his beef with Don might cause Elon to lose followers ... Lemon's a lot less sure. He seems to think Elon is uber-popular with his base, regardless.

BTW ... Elon's resorting to name-calling in this beef -- calling Don a "pompous fool" on X Friday before saying he's still got the right to share the interview on X when it drops.

Don's on his full rollout tour right now -- sharing bits and pieces of his interview set for release on YouTube and X on Monday, and he shared a particularly wild clip on "The View" Friday.

Check out the latest clip he dropped on "The View" ... Don asks EM if he values women and minority pilots less than men, and Elon says no -- but he also cites replies on his platform as alleged evidence standards are being lowered to include them in the profession.

All in all, not really a great look for the X CEO ... and it seems like this is just the very tip of the controversy iceberg.