Your thought processes seem to be right. I could suggest that you write to the LCD within the interrupt during the interdigit blanking period. Doing the LCDout outside the interrupt may give you wierd results when there is a clash between the LCDout code and the LED code. Assuming you disable interrupts for an LCDout, there may be a visible flicker in the LED which may be bearable or even irritating depending on the severity.

To write to the LCD inside the interrupt, you could signal the write after preparing a message. The interrupt code would then handle the write and you will not see a perceptible flicker.

This technique is usually used in small microcontrollers to multiplex 7segment LEDs with upto 8 keys.