The register
The register lists LSG Group Limited in London as a licensed sponsor on Skilled Worker, an entry that goes back to at least 2026. The register records its rating as Worker (A rating).
At Companies House the business is Lsg Group Limited (company number 10358887), a private limited company incorporated in 2016, 10 years ago. The registered office is at 52 Jermyn Street, London, SW1Y 6LX, SW1Y 6LX. Its filed activity puts it in business services. It has traded under other names before, including Lsgre 2 Limited.
A licence says an organisation may sponsor; it does not say it is hiring today. The way to find out is the same as for any employer: the careers page, the job boards, and a direct approach with a UK-style CV that says early that sponsorship would be needed.