I work for IBM on the Support Education Team. To confirm Rupert's answer, I'll re-paste his answer and insert comments in bold.
In an on-premises Notes/Domino environment, there are two main mechanisms for adding corporate disclaimers. The preferred approach is to use Mail policy settings to add the disclaimer at the client as this will be preserved during signing and encryption operations. It is also possible to set a server-side disclaimer using the Server Configuration document.
In LotusLive Notes Hybrid, the Mail policy settings approach is still available. Customer administrators do not have access to LotusLive server configuration, so the server-side approach would not be possible.
I am unaware whether LotusLive Hosted support disclaimers. Correct, not a feature.
Both models should support user-defined signatures in the same way as on-premises Notes/Domino does. The only Domino tool I am aware of to enforce a specific signature format is Crossware. This is a server-side tool, and so would not be available for LotusLive users. As far as signatures, it depends on what you mean. Each person can sign and encrypt mail messages. Is this what you are referring to? If not, please clarify with a response. Thanks.
Vinny Del Signore