The license of the combined work is under LGPLv3, but the individual code parts is either under LGPLv3 or Modified BSD License (or LGPL+BSD for short).
Its correct however that one can not remove the actually license text from the BSD licensed code. Doing so would be a license violation of the BSD license terms #1.
This is the good part about BSD for FOSS projects. One do not need to do any active action to be in compliance with the license. Do changes, add any licenses, and so long the license text on the BSD source code is intact, you are in the green.