It possible he needs more salt, so try two mugs of Bovril per day or even better a stock cube dissolved in a mug of boiling water.
If the issue is salt an improvement should be seen within a few days, then you can make bone broth with added salt instead of using a stock cube.
And see the GP for a full test of blood tests, also maybe worth stopping the satin to see if that helps.
I seem to suffer from tge same problems, I live n France and I am going to see my GP what test shoukd I ask for please, I do not take statins but rouge ritz which is natural and vety vety good.
I agree with above, insist on a full set of bloods. LCHF usually can lead to less thyroxine requirement, so ensure this is measured, however severe tiredness is related to under active thyroid, so I would suggest medical intervention rather than trial and error.
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Thanks for the thanks
Geoff