The lieutenant governor acts as a member of the:

House of Representatives

Cabinet

Senate

all of these

"Senate" is your answer

The lieutenant governor that is filled by the highest officer will become the state Senate. An example of this is in Tennessee, the full title of the leader of the Senate is "Lieutenant Governor" and and " Speaker of the Senate ". Another example of this is in West Virginia, the title of Lieutenant Governor is assigned by statute to the Senate President.