If I am Lost in Time and Space during a reckoning effect resolution, do I continue to resolve remaining reckoning effects?
I have changed my mind but I have no official ruling on this.

In general, you have to resolve all the reckoning effects and order should not matter.

However, during a reckoning: If you are devoured, that would end your turn right there. If you are either killed or driven insane, that does end your turn. Thus, it would seem logical that Lost In Time and Space would end your turn as well. 

Thus you would not be doing any reckoning events after those ones.  You dodge those bullets for this turn.

Lost In Time And Space was added in an expansion, I am not sure if this is covered by the FAQ or not.

Even going by the golden rule of cooperative games: If a rule can be interpreted in several ways, the right one is the least helpful to the players, the reading would be that yes, you stop doing any reckoning events once you are Lost In Time And Space.