Reading consecutive two pulse periods continuously
An interrupt off of one of the timers sounds like the easiest way to go. To get a measurement precision of, say 3% at 4ms means sampling every (4000us * .03) = 120us (8.333 KHz). If your code has little else to do, you might get away with clock-watching - micros() ticks every 4us - but you'll need to keep anything else you do between reads of micros() to under 120us, and half of that might be a good target figure.

In this answer I described a general non-blocking procedure for managing several tasks in a timely way. If you chose such a design, one task might manage the potentiometer and analog output, another one the RPM measurement, and another the LCD. The ISR would do nothing but set a flag. 

The RPM &amp; LCD tasks can run at a relatively low rate as they're intended for human consumption only. They may have to work piece-wise, though, to meet their time restrictions.