Hi Michael,
You can push an update from Solution Manager (the data supplier) to the SLD in transaction RZ70. There should be a button labeled "Start Data Collection and Job Scheduling". If your jobs are scheduled and everything is set up correctly, then starting your data collection will force an update ahead of schedule. (By default, the update is scheduled every 720 minutes -- i.e. 12 hours).
On the Java side, you need to push via the Visual Administrator (when you're at NW 7.02, that changes in 7.3 to the NWA), but you didn't ask that.
Typically, LMDB grabs an incremental update from SLD every 10 minutes or so. Check for a job called SAP_LMDB_LDB_0000000001. If your SLD-LMDB connection is not working properly, you may need to reset it. (SOLMAN_SETUP (as solman_admin or equivalent). Then system preparation -->5 Prepare Landscape). See SAP help on this Synchronization Between SLD and LMDB - SAP Solution Manager - SAP Library.
I hope this helps!
Best regards,
--Tom