Can i use a 6amp lutron caseta light switch with a 15amp breaker?
The switches are rated for the load they can carry ....it has nothing to do with your breaker rating.
On a fifteen amp circuit you could run multiple lights so long as the sum of all the lights currents (when on) does not exceed 15 A. 

For example at maximum load, if you had to run a string of 150 W incandescent lights. 


You could run 12 of them on your 15 A circuit and not exceed the circuit breaker rating.     
However you could only control a maximum of 4 of the lights with each 6 A light switch.


There is lots wrong with the example above since incandescent lights draw a surge current ....but I ignored that for the example ...I hope you understand the objective.

So in your particular case, where you didn't specify the number or types of light fitting you are connecting ....you need to ensure that the total load current on each switch is under 6 A ....and that the sum of your multiple cicuits does not exceed the 15 A circuit rating.