When opening Electrum, the bottom of the window showed message "Server is lagging (9 blocks)".
What does this mean? Is the Electrum server not up to date with the blockchain? Can I expect the problem to resolve itself quickly?
The message informs you that the Electrum server your wallet client is connected to is not in sync (not up-to-date) with the blockchain. In the message you quote it is 9 blocks behind.
This can happen when a server has been rebooted after maintenance or, in some cases, if the server is malfunctioning. Hence, there is no guarantee that the problem will resolve quickly.
While the server is lagging the blockchain, it is unable to provide your connected wallet with an accurate transaction history.
By default, Electrum connects to a random Electrum server on the network. To connect to another server simply exit and restart your wallet, or you can go to Tools > Network and manually specify a preferred server.