The spleen would be shown in an abdominal CT scan right? So if lymphoma spread to spleen it'd show up?

Maybe. The spleen is seen on ct abdomen. If there is a large involvement of lymphoma in the spleen it may be seen. There is also normal variation in spleen size, so there is not a binary cutoff for spleen enlargement in a given person. Often in cancer and lymphoma we depend on the overall picture and multiple tests to determine what is going on. And sometimes we only figure it out over time.
Most likely. The ct scan will show if the spleen in enlarge and irregular, which will usually help to decide if it involved in lymphoma. There are some exceptions, which can only be known through removal or biopsy.