Can different sized conductors be used in a lighting circuit, such as 12/2 from panel to first switch box and 14/2 to the individual lights?

the conductor size needs to correspond to the size of the overcurrent protection device...
i.e. if you have a 15 ampere circuit breaker = 14 AWG
if you have a 20 ampere circuit breaker = 12 AWG
There is a table in the electrical code that provides this information...

To say it more simply, yes but why would you want to do that? The largest breaker you could use would be 15 amp.

To say it more simply, yes but why would you want to do that? The largest breaker you could use would be 15 amp. This is your answer. You can, but why would you??

While this is mostly used on CATV and low voltage applications, some people use a larger wire to get to the first outlet IF it is a long way to the outlet. Called a home run. This does protect from voltage drop. You must, however, use a breaker for the smallest line. So, if you start with a 12AWG and then to 14AWG, you would need a 15 Amp breaker. I have only seen it done when the first outlet was greater than 25 ft. away from the breaker box.

While this is mostly used on CATV and low voltage applications, some people use a larger wire to get to the first outlet IF it is a long way to the outlet. Called a home run. This does protect from voltage drop. You must, however, use a breaker for the smallest line. So, if you start with a 12AWG and then to 14AWG, you would need a 15 Amp breaker. I have only seen it done when the first outlet was greater than 25 ft. away from the breaker box.Just a quick comment. This becomes more important when the distance reaches more like 100'.
In pretty any average home voltage drop is not even worth thinking about. And in larger homes standard practice is to place sub-panels in strategic locations so typically branch circuit VD is not an issue either.
I was in a 15,000 square foot home yesterday and it had a 600A service with three main panels and five sub-panels.