No, you don't need a missal to attend the Latin Mass. Missals are great if you want to read all of the propers of the Mass, but they're not essential, especially for first-timers. Most priests read the Lesson/Epistle and Gospel in English anyways.
We generally recommend that new-comers simply observe the Mass before attempting to follow along in a missal. You'll be able to follow along with a missal even more easily after you've been to a Mass or two.