I have had all my HSA accounts through my employer, usually tied to my medical insurance (HDHP). Every time I switch employer or the insurance changes or the HSA provider changes, I consolidate the money from my older account to my new HSA account.
IMO I think lively is good for individuals as there is no fee (I know there are other providers with no monthly fee). But I wonder why would my employer use this service if my insurance provider offers linked HSA and auto-pay for the claims?