I don't know if this is a difference between AE and BE, but "a lot has been built up" sounds natural to me. I think "a lot" can be used without "of" even when it's not being used as an adverb. For example:
A lot has been written about the Cold War.
A lot is at stake.
His actions say a lot about his character.
But in "When I lived there the street was considered part of the outskirts of the city. Nowadays, a lot has been built up." there is nothing that 'a lot' refers to. In two of those short sentences there is a reference:
A lot has been written about the Cold War. Not: A lot has been written.
His actions say a lot about his character. Not: His actions say a lot.
You could certainly have 'A lot has been written' or 'His actions say a lot' as complete sentences, but only in a context where the reference of 'a lot' is already known or about to be described.
'A lot is at stake' describes a state, so the reference is to 'at stake'. That isn't really comparable to the other sentences.
For me, the OP sentence needs more information or a different structure to make sense. What is the 'a lot' that has been built up? I'd have no problem if there was relevant context. At the moment we have the street containing homes being part of the outskirts of the city - so it is already a built-up area. Let's reword it:
"When I lived there the street was considered part of the outskirts of the city, next to open fields. Nowadays a lot has been built up."
Ah yes, it's the open fields that have been built up.
Yes, TT, I think so. If I see "a great deal has been written" I can see that it is a true statement, but one which is devoid of any useful meaning without further context. "Deal" is, of course, another word (like lot) that has more than one meaning, so I should make it clear that I am not referring to a use like "He made a great deal" referring to a business transaction.