Questions & Answers about Lunedì, se non piove, vado in biblioteca a piedi.
They usually are lowercase in Italian: lunedì, martedì, mercoledì, etc.
Here it is capitalized simply because it is the first word of the sentence. So inside a sentence you would normally write:
Vado in biblioteca lunedì, se non piove.
Also notice the written accent: lunedì ends in an accented -ì.
Italian normally uses weekdays without an article when talking about one specific Monday:
Lunedì vado in biblioteca. = On Monday / Monday I’m going to the library.
If you use the article, it often means a habitual action:
Il lunedì vado in biblioteca. = On Mondays I go to the library.
So in your sentence, lunedì refers to a particular Monday, not every Monday.