Can I implement a LFM method on an Arduino?
Since you are talking about Arduino, I suppose you want to do it digitally.

The answer is: it depends.

It depends on:


Desired frequency of the carrier
Desired maximum frequency of the input signal
Desired accuracy (compared to the equivalent done with analog components)


But in general I'd say that it's unlikely it will have sufficient computational power. I'm assuming the question is for the 16MHz 8 bit UNO.
The Cortex M3 on the DUE might stand some chance, being a 32bit core @ 84MHz.

It might be possible to do some trick using a PWM signal and a digital output with a wired AND, but I'll leave to others to comment about its feasibility.