Well, you put the LGPLed code in a separate source file. And you
reimplement it in yet another source file, while gradually deleting the
LGPLed functionality.
There is one catch though. The BSD licence allows people to make proprietary
changes to the code and does not mandate any code sharing with others.
When you mix BSD and LGPLed code, at least the LGPLed code must be
shared with others AND the binary must be distributed in such a way that
the LGPLed code can be changed, compiled, and relinked into a functional
binary.