Issue :-

On Lync edge server, Cannot Start Lync Access Edge Server - %%-2146762487

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Solution :-

This issue is caused due to the certificate miss-match or absence of required certificates.

it showed that the Public certificate had issues and need to reinstall the same. It is due to deletion of the root cert (internal CA1). Reinstall the certificate and restart the services. Please make sure all the edge external services FQDN in the public certificate SAN list. You can have a try to reinstall the public certificate again. Delete the external public certificate from the Edge server certificate folder in MMC. Then import Certificate again in the Certificate Wizard and assign the certificate to the External Edge interface. If the external services port is grabbed by other application, it also would cause this issue. Please have a check.