Have previously discussed this particular situation with an examiner; the initial query being in what seat the LPC must be done from (captains or could it be done in the instructors seat in the case of an instructor sitting the test?) We came to the conclusion that it could be done from either seat.
The problem comes from the fact that the instructor renewal test, whilst demanding precise flying, is only really a test on competency of instructing, and usually only encompasses one or two sections of the course. (ie. brief/fly an ex.6 or similar). The LPC must contain all the relevant sections on the examiners form eg. limited power, engine offs, hover square etc.
If the examiner for the instructor renewal is made aware of the need to also carry out an LPC, it may be possible to carry out a slightly extended flight to ensure all sectors for both instructor and LPC are carried out, thus enabling both to be 'signed off'
Hope this is of help.