The register
The register lists Livy U.k. Limited in London as a licensed sponsor on Skilled Worker, an entry that goes back to at least 2026. Rating on the current register: Worker (A rating).
Livy U.K. Limited is the registered name (Companies House number 12454749), a private limited company on the register since 2020. The registered office is at C/O Weightmans Llp, 105 Fenchurch Street, London, EC3M 5JG, EC3M 5JG. Its filed activity puts it in retail.
Holding a licence is the expensive, slow part done. For Livy U.k. Limited the question each time is only whether the role and the pay fit the current rules, and that is checked per vacancy.