One cannot use Menü---it is what is called Prix Fixe, the french word that English speakers use for a special set meal that usually includes soup or salad, a main entree, and sometimes a dessert for a set price. Better> die Speisekarte. At fast food places, Menü can be used for the pizza, salad, drink combo, etc.
Pronunciation of lese. "lay-se" or "lee-se"? I'm sure I've heard it both ways, so often get confused. Here the lady says "lee-se", so I incorrectly spelt it "liese", even though I do know it is spelled "Ich lese" but the pronunciation keeps throwing me off. Are both ways correct, does it vary depending on the speaker?
German "E" makes a sound like English long "A", except that in English it's a vowel glide ("ay-ee") and in German the sound is pure without the glide into the "ee" sound. The variant sound sounds just like English short "E". English long "E" is always wrong. The S in "lesen" should also make an "z" sound. The "e" in the final "-en" is a schwa, which is an unstressed "uh" sound.
If by "the lady" you mean "the computer synthesized text-to-speech used on Duolingo", she's using the "ay" sound but it does sound very much like "ee". Keep practicing lesen, ich lese, du liest, er liesst, sie lesen, and you'll be a natural in no time. :)