Study the contents of a transport request for an entire project as generated by the LSMW standard functionality. You'll find the table keys of all relevant LSMW tables in there.
Look at the primary keys to understand which tables are relevant for project, sub-project and object level.
Use available (but not released) TR_... function modules to prepare the desired tables keys for your transport, search for related SCN discussions and information.
Be aware that by just transporting an LSMW object you might face inconsistencies in the target system, for example when a fixed value or conversion rule is being used which is not transported along, since they reside on project level.
Thomas