Dear all,
with a little delay, I can mention the problem is solved meanwhile.
1) I made manually a connection on the LanSweeper server to the trusted forest using the net use command and the appropriate credentials. From that time the LSserver could access and scan all workstations in that trusted domain.
2) Finally I found the root cause. In the home forest there had been a DNS entry created in the very past, before the trusted forest was created, with same name as this forest but pointing to a web server instead of a domain controller. After removing this conflicting DNS entry the problem was finally solved.
I also would like to thank the LanSweeper support team for the hints and tips.
Best regards
dirkv.