YCT is Orthodox; I know a number of students there. And I know a Lakewood-trained rabbi who has had YCT Rosh Yeshiva Dov Linzer give shiurim at his shul.
I personally think joint appearances with rabbis from two yeshivot that have different hashkafot is very dangerous. If we religious Jews actually can get along with each other while disagreeing, that might bring mashiach. We can’t possibly permit that!