"That is a lot of meat."
Translation:Dat is veel vlees.
There are ways to translate "a lot (of" using een, but "veel" is not one of them. Just pointing that out.
Besides "veel", you could use "een heleboel", "een boel" or "een hoop", which all use "een".
But I think most people just say "veel" to mean "a lot (of)".
'vele' is used with plural nouns:
In de bossen rondom zijn vele wandelpaden, die lopen tot aan de toppen van de bergen, waar prachtige panorama's je blik verruimen.
In the surrounding forests there are lots of hiking trails which run to the tops of the mountains where stunning panoramas give you a fresh new perspective.
The modern model of grammar assigns veel to be a determiner, rather than to be an adjective, since it refers to the number of its subject, rather than modifying its size, color, type, etc.
Vele is the definite form and is used when referring to a specific lot, which is typically accomplished by using a definite article. Veel is the indefinite form, and is applicable here.
I personally prefer to think of veel, weinig, and such as being determiners rather than adjectives, because no exception to the rules of inflection/declension are then required. Enough exceptions!