Comic book Adamantium, No!
Adamantium has been only melted by a high frequency sonic arm and bended by magneto. But not by brute force if heat like a Lightsaber. A weaker version of Adamantium couldn't be broken by a super angry Hulk and Thor working together!
Now, a Lightsaber is very powerful but it CANT cut through anything. In Empire Stikes Back a Lightsaber hits Darth Vader's armor but does not cut through it. Also boba fett's mandalorian armor is strong enough to block Lightsabers. A Lightsaber wouldn't be able to cut through Adamantium.
Movie Adamantium, maybe!
This is us because Movie Adamantium has been cut before.
It has been cut by a super heated Adamantium blade. Because a Lightsaber is just a laser, with enough force (pun intended) it might be able to cut through Adamantium!