Can diet affect my spinal stenosis?

Not really. Diet can affect a lot of things, but once you already have stenosis, diet has little or no effect with the exception that carrying extra body weight can certainly make it more symptomatic.
Yes. Getting obese can lead to increased lumbar degenerative changes leading to further narrowing of the spinal canal leading to increased degree of spinal stenosis.
No. Aside from keeping weight well controlled, diet should not play a major role in spinal stenosis.