I would view this in the other direction--meaning the employer should take steps to immediately remove all §213(d) expenses from the LSA. And also look for a new LSA TPA for not flagging the issue!
I suppose in theory you could offer COBRA for the LSA, but it is not clear how that would operate given (as you noted) there are health and non-health components to the plan. I think you could treat it like an EAP and make all types of benefits (including non-medical) available through COBRA, or try to segregate a medical-only component that is accessible through COBRA. I'm doubtful the TPA could do that, but in theory it could work.
To me that would be the least of the concerns, though. Think of all the issues with the LSA that could not be readily addressed:
ERISA plan doc/SPD
HIPAA privacy/security
PCORI fees
§105(h) nondiscrimination
ACA reporting
ACA integration to satisfy market reform provisions
HSA eligibility
Multiple CAA potential issues
So I would recommend against trying to shoehorn a COBRA approach into this, and instead reverse course on the medical benefit inclusion asap.
More details: https://www.newfront.com/blog/lifestyle-spending-account-compliance-considerations
Slide summary:
2025 Newfront Fringe Benefits for Employers Guide