No. if Lauda is excluded from DT1, he cannot be on DT2.
Lauda is blacklisted from DT1 (not excluded), and is still on DT2 (
proof).
He wiped his trust&distrust lists
a couple weeks ago and washed himself out.
Wiping your trust list only disqualifies you from DT1 when Theymos does his monthly update. It does not instantly disqualify you. However, when Lauda was removed from DT1, it was not the result of Theymos doing an update. Lauda's removal also was not the result of more people on DT1 distrusting her than trusting her.