(1) We had alot of difficulty in finding the place.
(2) *We had lot of difficulty in finding the place.
(3) We had alot of difficulties in finding the place.
(4) We had lots of difficulties in finding the place.
(5) *We had lot of difficulties in finding the place.
Singular "lot" requires "a" as determiner, as in (1) and (3), so (2) and (5) are ungrammatical. Plural "lots" requires no determiner as in (4).
(6) There are many people here.
(7) There are fifty people here.
(8) There is one people person here.
(9) There is much are many people here.
"People" has only a plural interpretation here, so (6) and (7) are okay, but in (8) singular "one people" is ungrammatical; instead we have "one person". Count nouns like "people" take "many" as determiner, but not "much" which is used only with non-count nouns.