After being in chorus for four years, memorizing lyrics gets pretty easy once you know what you're doing. Find the lyrics, and you need a steady rhythm to keep on track. If you have a basic grasp of music, you should be able to pat your leg to the beat of the song pretty accurately (unless you're tone deaf, but I doubt you are). After that, you just have to practice. Songs are basically poems with music and rhythm, but instead of stanzas, they have bridges, verses and choruses.
I've added a simplified diagram of the structure of a song (I just found a random song that is most people know). As you can see, songs can be broken down into pretty simple little things and most songs follow the same structure.
So find the song you are singing, get the lyrics and have a visual, physical copy of them. You must listen to the song and practice. You can even ask your friend to record himself singing the song, and give you the recording so you have an auditory example of the song to practice with.
After you think you have memorized the lyrics, test yourself. Try to sing the song only with his accompaniment, do that until you have no auditory mistakes. Then do it with only the lyrics in front of you, do that until no mistakes in rhythm is made. Then after you have done that a few times with no mistakes, do it with neither. After you do that, you will have memorized the song.
But if you wanna take the easy route out (with this method, there is a higher risk of messing up during your performance, but it is quicker and easier) then just sing along with him until you memorize the song.
Good luck! :)