We're migrating to fully Exchange Online (No Hybrid) from Exchange Server 2013. Due to the environment (multi-national) complications, we're planning to use a 3rd party tool for the mailbox migration but it looks like the tool can't migrate Exchange DLs, Groups etc.. but mailboxes only. What are the native options we can use in this case?
There are no native "migration" tools. You either synchronize them from on-premises, or recreate them directly in Exchange Online. This module can help you automate the latter: https://github.com/timmcmic/DLConversionV2