Similar to Cheers, L'Chaim is a Jewish toast said before drinking meaning "To Life!" just as stated in the song. L'Chaim is a phrase that is at least 2,000 years old. The word in Jewish has an ending meaning "two" refering to both the current life here and the next life as well. This is typically stated at weddings, special celebrations as well as other moments when it is called for.
Another reason that is believed L'Chaim should be stated before drinking alcoholic beverages specifically is due to the number of religious passages that involve unfortunate things happening after drinking wine.
"To Life" is a song sung just after Tevye and Lazar Wolf have agreed that Tzeitel will marry Lazar Wolf. The two are celebrating and the whole inn joins in the celebration of the current life and the life to come.
Jewish English Lexicon. (n.d.) l'chaim. Retrieved from: https://jel.jewish-languages.org/words/301
One for Israel. (1 Jun 2016.) "L’CHAIM!" THE DOUBLE BLESSING OF THE HEBREW WORD FOR LIFE. Retrieved from: https://www.oneforisrael.org/bible-based-teaching-from-israel/double-blessing/
Reform Judaism. (n.d.) Why do some Jews say “l'chayim” when making a toast? What does the word actually mean? Retrieved from: https://reformjudaism.org/learning/answers-jewish-questions/why-do-some-jews-say-lchayim-when-making-toast-what-does-word
Shurpin, Y. (n.d.) Why Do Jews Toast L’Chaim—To Life? Retrieved from: https://www.chabad.org/library/article_cdo/aid/2987145/jewish/Why-Do-Jews-Toast-LChaimTo-Life.htm