Here's an article on this:
Synonym’s current implementation relies on the Omni Layer, a decentralized asset protocol for Bitcoin, and OmniBOLT, which ports that layer’s functionality to Lightning channels.
An Omni transaction is a Bitcoin transaction with extra metadata, meaning it doesn’t require a separate blockchain that alternative protocols for asset issuance commonly leverage.
There is still much work to be done on Omni and OmniBOLT to consider the token-on-Lightning functionality ready to be released.
Synonym plans to release a mobile wallet and a browser extension wallet in the coming months that will support tokens on Lightning and Slashtags, a web-of-trust-like protocol the company teased last year.
USDT Pilot Brings Tokens To Bitcoin’s Lightning Network https://bitcoinmagazine.com/business/usdt-pilot-brings-tokens-to-bitcoin-lightning
And another article:
The benefits of using USDT on Lightning include lower transaction costs, increased privacy, and speed. Stablecoins on the Lightning network have the potential to empower circular economies, where Lightning is the primary means of payment and alternatives are no longer needed.
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