Militia could be and were turned over to Confederate service. For example, in March 1862 two ninety-day Alabama regiments were turned over to Confederate service at Mobile AL. The 3rd and 4th Alabama Militia Regiments served for sixty days and disbanded.
To the best of my knowledge, the Louisiana Native Guards were disbanded when the Louisiana state legislature reorganized the militia in January 1862. By law afterwards only white citizens could serve in the state militia. In late March 1862 Governor Moore called upon the Louisiana Native Guards to return to their former organization and help defend the City of New Orleans. Evidently most former Native Guards remained in the city when it was evacuated, bringing an end to the brief history of this militia command.
Prior to being disbanded, I see no evidence that Governor Moore turned control of the Louisiana Native Guards to Manfield Lovell.