It was possible to make use of bitcoin blockchain for omini layer, but that is onchain. Lightning network is layer 2 and it is not on chain but off chain. If USDT wants to be able to do that, its developers needs to create off chain layer 2 means of transferring USDT, but they may not want to do that because of altcoins blockchain options which have low transaction fee.
Thanks to Taproot, it is quite possible to issue USDT or other tokens on the Lightning Network. Check the project by Lightning Labs called Taro: