Is there a word to describe the feeling of the lump in the throat due to nostalgia? If so, what is it?
I don't think it's very common, but I've heard people use the word verklempt to describe this feeling.
Verklempt is a Yiddish word that means "overcome with emotion." Pronounced "fer-klempt," people use it when they are so emotional that they're on the verge of tears or at a loss for words due to their emotional state.
I'm not sure if this progression is universal, but a particular experience could induce a pang of nostalgia, which, in turn could cause a person's throat muscles to clench up and create that "lump" sensation you are describing.
In terms of how to describe that feeling in the throat, calling it a "lump" is the word commonly used to describe the sensation. If you want a verb, I would suggest clench.
Globus ( -pharyngis)
a feeling of a lump in the throat
Globus is the medical term for a sensation of a lump in the throat where no true lump exists. It was once called Globus Hystericus, wrongly suggesting that this is a psychiatric condition. Globus is sometimes also referred to as Globus pharyngeus (pharyngeus is simply the medical term for the throat).
Wikipedia entry for Globus pharyngis includes psychosomatic factors to Globus:
In some cases the cause is unknown and symptoms may be attributed to a psychogenic cause i.e. a somatoform or anxiety disorder. It has been recognised as a symptom of depression, which responds to anti-depressive treatment. [emphasis mine]