Hmm... I think, this way you should construct a program-controlled expansion to P1 and send/receive data first to keyboard, then to LCD. I had the same problem with lack of ports, when expanding RAM, ROM and net-card

But it will cost you few milliamperes and free space in your kit.

EXAMPLE:

; make a tick to activate your interface
setb P1.pin
clr P1.pin
mov P1, #data

; make a tick to deactivate your interface
setb P1.pin
clr P1.pin

pin means port's pin and at the same time number of expanded port P4,P5,...,P11