Well, it is advisable to use the version, when booting from external media, which is the installed version.
But you really shall not use an older or vastly different (i.e., far newer) version.
(IIRC, I phrased this carefully in my guide to extend the root volume size.)

Side note: This is the same for all Linux computers, be it a PC, Notebook, Phone, whatever! Please refrain from using "anything that boots". While the on disk format of LVM and classical file systems should stay the same and changes always shall be upward compatible, nobody tests with vastly different versions of the tools to modify them (LVM and FS resize), so subtle incompatibilities may occur. And mind that you modify with newer tools (externally booted) and then boot the installed OS with the old versions, so upward compatibility is not sufficient.