100ms for setting up an initial TLS connection is about what I'd expect. It depends on the key size, ciphers, etc, but up to 300ms is typical.
However, this should only be done at the beginning of the connection. After this the client will have a symmetric encryption key that is much faster to use. Their load balancer should be caching these sessions so that subsequent connections don't need to re-negotiate a session key.
If this 110ms is only on the first request, and a cache miss on the sessions, then I'd say that's probably something you should be expecting. If it's after the TLS session has been set up, or on a cache hit, that sounds bad. It also could be that their session cache isn't large enough and is forgetting sessions too soon, causing more TLS negotiation than may be necessary.
However, this should only be done at the beginning of the connection. After this the client will have a symmetric encryption key that is much faster to use. Their load balancer should be caching these sessions so that subsequent connections don't need to re-negotiate a session key.
If this 110ms is only on the first request, and a cache miss on the sessions, then I'd say that's probably something you should be expecting. If it's after the TLS session has been set up, or on a cache hit, that sounds bad. It also could be that their session cache isn't large enough and is forgetting sessions too soon, causing more TLS negotiation than may be necessary.