Vpp of oscillation of LCR circuit
C2 brings nothing to the party because it directly connects across the voltage source. 


  Then what is the relationship between Vpp_L and LC combination?


The "ringing" waveform amplitude is due to L, C and R values. Together these form a tuned-filter with a certain damping ratio. That damping ratio is governed by L, C and R and, the lower the damping ratio, the higher the ringing waveform amplitude.

If the resistor value is low (say 1 ohm): -



You get a small amount of ringing because the damping ratio (\$\zeta\$) is 0.3536. However, if R gets bigger such as 31 ohms you get this: -



Clearly the step response is much more animated now and, at 1000 ohms you get this: -



Interactive tuned circuit page. This website also gives you the mathematical tools for working this out algebraically so, if you want instead to apply a step input where the rise time is significant you can use Laplace transforms. 

Alternatively just stick with the simulation and note that broadly speaking, if you keep the product of L and C constant and vary R you can alter the ringing voltage amplitude. If you wanted to changing the ringing frequency make L or C or both bigger in value.