If I may add a context to your sentence to explain to you the difference: * "Surprisingly, we had AN English lesson yesterday." This implies that English lesson may not be a part of your curriculum and you were taught of it surprisingly. * "Surprisingly, we had THE English lesson yesterday." Here, given the fact that English lesson is part of your curriculum but you didn't expect that it will be taught yesterday (It woould have been math or science for instance). :)

If I knew that you were studying English and that you were taking an English course, I could ask you, "When did you have the (or 'your') last English lesson?" and you would answer "I had the (or 'my') last E lesson yesterday." But, if I did not know that your were having E lessons, then I would ask, "Have you ever had an E lesson?" and you would answer, "Yes, I had an E lesson yesterday".

2) "an" 3) "the" would be correct only if you were going to have a single lesson, and that lesson is now complete.