Partly in response to a recent PM from Rémi:
Attached is a service note from Sam Reaves of the LeCroy dedicated groups.
It is for the 9354-4 PLL, I think this should apply to the LC series too.
As for being sure that the SH clock is the cause: You'll need some way of checking that it goes unstable when warm, either a fast scope with persistence, jitter meter, S.A., frequency counter...