"the lamp and the apple"
Translation:a lámpa és az alma
"egy" is indefinite, "ez" is definite. For example, you are telling to your friend that you saw a good looking girl yesterday: "Láttam EGY szép lányt tegnap." It's just a girl, you don't know her, your friend also doesn't know. Another example: I saw that girl you were talking about: "Láttam EZT a lányt akiről beszéltél.
There's only a z if the next word starts with a vowel. Alma starts with a vowel so the apple = az alma, but lámpa and lány start with a consonant, so the lamp = a lámpa and the girl = a lány. It's like how in English we have a lamp and an apple; just don't get mixed up between egy/a(n) and a(z)/the.