It's close:
$ echo '-L/home/a -la -L/home/b -lb' | sed 's/-L[^[:space:]]*//g' -la -lb
Or, if you have no spaces other than spaces, just
$ echo '-L/home/a -la -L/home/b -lb' | sed 's/-L[^ ]*//g' -la -lb
You may need to remove extra spaces.
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