Ringing seen when a zener diode is used with series diode as a snubber
There is always junction capacitance in a diode, so both D1 and D2 have  capacitance. S1 and L1 will also have some parasitic capacitance adding more capacitance to the system . This will cause ringing with L1. 
As for real-life diodes, they usually also have a reverse recovery, https://en.wikipedia.org/wiki/Diode#Reverse-recovery_effect which can cause circuits to ring but these are usually not modelled in LTSPICE.