Close a circuit with one input signal
if you can use 2 (as drawn) or 6 (as written) of the outputs of the 8 provided on the M54564P, one for each LED, that would be one way to have them not paralleled.

Another would be to add diodes between a single the M54564P output and each LED. 

Faced with the updated problem 

It looks like you have only a single extra output, need to drive a single extra dependant load.  I would thingk that driving that with a dedicated output would be preferable to using the diodes.

your drawing shouws 2 unused outputs on the driver chip and if you have a spare output on the arduino to drive the apropriate input pin just do that.

6 diodes to save one output pin seems like a lot of effort unless you haven't got a spare pin