The thread, that, I linked to mentioned, that, the governor of Kaliningrad threatened to secede from the Russian Federation amidst Yeltsin's cries for people to take as much liberty as they wanted.
In such a timeline, Kaliningrad may secede from Lithuania like Transnistria did from Moldova.
The question then becomes whether this would be a mutually agreed upon break or not. I would hope that the Lithuanians would not try to overextend themselves.
An independent Kaliningrad might have more options than a Russian Kaliningrad, but would it be inclined to take them? It might well be another Belarus, as it were.