It also seems that it is not working with BNB neither
BNB is not ERC20 anymore so it is seperated from your ethereum wallet.
Have you tried to contact the Binance? Because if they are just asking an ethereum address for withdrawal of ERC20 from their exchange, then they will allow all ethereum address then Ledger has no problem at all.
UPDATE:Note when I tried to generate my deposit address in ZIL from Binance.

In your problem for withdrawing your ZIL from binance, it's probably Binance is using Main net of ZIL, which they want a main net wallet address of ZIL. If that so, you will really need a receiving address of ZIL from the main net.
Ask Ledger about adding mainnet of ZIL since as I can see on the
list is ERC20 of ZIL that's why you are getting an ethereum address if you are asking for ZIL receiving address and getting an 'invalid address' from binance withdrawal.