euny, if you go to the Mudcat Newcomers' Guide, you'll find links to several lyrics sites, e.g., Cowpie, Rabid Squirrel, OLGA (which no longer supplies lyrics, only guitar tabs), Lyrics World (which I'm not sure is still operating). Also try a Google search using the term "song lyrics." You'll be directed to a lot of sites.
Rabid Squirrel does have lots of lyrics from the 30s and 40s (though, as with other member-supplied info sites on the web, the accuracy sometimes leaves something to be desired).
If you are in a moderate to large metropolitan area, your local library will probably have a number of sheet music books for songs of the 1920s, songs of the 1930s, etc., as well as books like "Favorite Rodgers and Hammerstein Songs," "Big Band Hits," "Songs of The War Years," etc. I've collected lots of sheet music this way, and the accuracy of the lyrics, chords, melodies, etc., is probably better than what you find at most online sites with free info.
If you do have specific songs you're looking for, you can probably find them by doing a DT/Forum Search using a key phrase from the song or by using the Mudcat "Filter" box, typing in a key word from the song title and setting the filter for 3 years. You can also start a "Lyr. Req." thread and give the titles you are looking for, if you don't find them already in the Forum somewhere.