As a determiner, any implies "some, at least one, or one kind"; permits either singular or plural, depending on the context; and does not carry any number in itself:
1.0 [USUALLY WITH NEGATIVE OR IN QUESTIONS] Used to refer to one or some of a thing or number of things, no matter how much or how many:
[AS DETERMINER]: I don’t have any choice.
[AS PRONOUN]: Someone asked him for a match, but Joe didn’t have
The city council ceased payments to any but the aged.
2.0 Whichever of a specified class might be chosen:
[AS DETERMINER]: These constellations are visible at any hour of the
[AS PRONOUN]: The illness may be due to any of several causes.
Notice that the "pronoun" use is an implied reduction of the determiner use:
Someone asked him for a match, but Joe didn’t have any [matches].
The city council ceased payments to any [people] but the aged [people].
The illness may be due to any [cause] of several causes.
Any has generally two uses. [See: The Cambridge Grammar Of The English Language, pages 381-385.]:
- As a non-affirmative determiner, any is used with plural nouns and
uncountable nouns to indicate existence of some or at least one in an affirmative question; and it indicates non-existence in a negative statement or question.
- Do you have any cigarettes?
- I don't have any cigarettes.
- Can't you buy any cigarettes?
- Do you have any money?
- I don't have any money.
- Can't you borrow any money?
Sentences 1 &2 are existential statements, so the singular noun in sentence 1. sounds foreign, and plural noun in sentence 2. is native. There are some situations where a singular count noun might work awkwardly, but the indefinite article a/an is preferable:
I don't have a cigarette.
I don't know a native speaker.
According to Huddleston and Pullman, there is a proportional use of non-affirmative any where the singular count noun works as well as the plural:
Sentences 3. and 4. seem to fit comfortably into that sub-category, but some would argue that they fit into the second use of any below.
- As a free-choice determiner, any can be used with singular or plural nouns as well as uncountable nouns:
- Any native speaker can hear the difference.
- Any cigarettes you smoke will shorten your life.
- Any coffee tastes good in the morning.
No problem either way: Evidence is an uncountable mass noun (it used to have a plural form, which is now declining toward extinction); a single witness with other evidence would be sufficient, but more witnesses can be better; the lot is a singular reference to a group of items.
The lot seems to be in apposition to evidence, and witness. The missing articles and the deleted and are an informal reduction that mimics the way people speak. Since the leading phrase: We've got him dead to rights is also informal, the entire sentence sounds more like colloquial speech than formal writing--whether you use witness or witnesses.