Having owned an LX200 and having had exactly the same problem, yes, re-centre and re-shim, and re-collimate on completion.
You may have to be a bit iterative as it's a fiddly job inserting shims, not to mention getting or making shims of the right thickness.
I found having the LX200 in the mount and oriented so that the OTA was pointing straight upwards (so that the corrector was flat and at a comfortable working height) made the job easier.
You should notice an improvement in image quality - an off-centre corrector causes a sort of permanent astigmatism (at least that's what it looks like to me).
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