Lawson 10x/Ming.le + multiple domains?

Which authentication option are you using -- Kerberos or LS as STS?
if you're using LS as STS, then ldapbind doesn't change.

Can it be done using Kerberos?

Are you talking about multiple AD domains within a AD forest, multiple search containers within a single AD domain, or multiple AD servers within a single AD domain (i.e. for failover)?

For the first option, I haven't tested it, but it should work, as long as the LSF/WebSphere and SharePoint/Workspace servers and their primary AD logon server are in the SAME AD domain.
For users in AD domains in same forest (i.e. trusted domains), the trust relationship between them in AD is what allows them to authenticate, since both SharePoint and the delegation user specified in WebSphere can process the Kerberos ticket assuming the trust relationship is set up. (Authentication is handed via SharePoint/Workspace, and then the Kerberos ticket is forwarded to LSF/WebSphere, which uses a delegation user.)

For the other options, since authentication is really done via SharePoint, regular SharePoint rules apply, so those should work as well.

Again, I haven't tested any of these extensively, so can't say for sure.

Hopefully that's what you asking...

P.S. why do you always ask such hard questions ?

LSF and Mingle server are on - abc.com
"outside" trusted domain - 123.com
another "outisde" trusted domain - xyz.com

They are totally independent to each other besides being trusted.