“Those rabbonim were in contact with Mr. Lieberman only before he went off the derech and became an apikorus by joining the Conservative movement.”
Not true. I have personally seen copies of some of the correspondence between Rav Soloveitchik z’tz’l and Rav Lieberman z’tz’l from the 1950s when they were trying to set up a joint beit din across Orthodoxy and the Conservative movement. Interestingly, it was the Conservatives who backed out. The Rav would never have agreed to serve on a beit din with an apikorus!