Frequent exposure to X-rays will damage your living cells, which is why radiography staff retreat behind shielded areas, as the cumulative effects of exposure could be harmful when one is exposed to X-rays day in, day out.
However, it is important to understand that X-rays do not "impart radioactivity" to objects in contact with them, but are the result of radioactive decay within an emitting source.
So, although X-rays could cause damage to the cells of a plant or animal, the lettuce and ham in your sandwich is effectively dead, and in no way can it "impart radiactivity" to you. Even if the cells of your lettuce or ham were somehow damaged by this brief exposure to X-rays, they will just be digested by your body just like any other food you ingest.
THEY ARE NOT RADIOACTIVE IN THEIR OWN RIGHT.
As an analogy - think of UV rays from the sun. These too are electromagnetic waves - and long-term exposure to these can harm your skin cells, causing melanoma cancers. Yet eating something exposed to UV rays can NOT give you cancer solely because of this exposure.