Answer
Yes — build a Saved Search for the second Custom Field's LOV that references the first Custom Field's current (live, in-page) value as its filter condition, the same way you'd build a saved search referencing any other field on the same form. To make that filtered saved search apply automatically as the default every time the LOV opens (rather than the user having to manually select it each time), go to the LOV's results pane, RMB > Properties, and set the dialog's startup behavior to use that specific saved search by default.