Are SPI or I2C timer interrupt based protocols?

I don't think that any code is necessary, I simply use Timer1 interrupts to generate TTL pulses with predefined period ranging from 100us to 1ms. It is very important that they are equidistantly spaced.

If I use in my code SPI or I2C to connect the LCD will that affect the Timer1 interrups? SPI can work on 4Mhz, right? So if the Arduino need to finish something over the SPI bus, that cannot be interrupted, but still 4Mhz is way faster than a default 9600 baud rate in standard serial protocol.