there is not a max dose for lantus or levemir; you will use the dose that works to get your cat's BG into a good range.
My two cats have acromegaly, and so they receive high doses.
Shadoe is going up to 8u tonite, and Oliver is currently at 20u BID.
If you are finding that your cat is needing an ever increasing dose, you may want to have your vet look into the reason for such a high dose.
What is the current dose you are giving and what are your cat's BG numbers?
edit to add:
just looked at ss now.
I see you increased to 5u; maybe give that dose a chance to settle, have the shed fill, and see what you get?
I was wondering if there was any chance that you could get more tests in so you can see what's happening around mid-cycle? It would be good to know what his nadir is, and if he is flat high numbers all through or if he is dropping low at some point and then bouncing.