Translation:There are a lot of people in this country.
Cambridge Dictionary: "We use a lot of and lots of in informal styles. Lots of is more informal than a lot of. A lot of and lots of can both be used with plural countable nouns and with singular uncountable nouns for affirmatives, negatives, and questions." http://dictionary.cambridge.org/us/grammar/british-grammar/quantifiers/much-many-a-lot-of-lots-of-quantifiers
"The first important difference is that 'many' can be used only with countable nouns in the plural, and 'much' can only be used with uncountable (mass) nouns in the singular. There is no such distinction for 'a lot of' and 'lots of', which can be used with both, i.e. both 'a lot of/lots of people' and 'a lot of/lots of water' are correct." https://jakubmarian.com/many-much-a-lot-of-and-lots-of-in-english/
An English teacher: "'A lot of people have worries about grammar' is correct." https://www.quora.com/Which-is-gramatically-correct-A-lot-of-people-has-or-A-lot-of-people-have/answer/Abi-Ru-Shirzan
"'A lot of/lots of' is still felt to be informal, especially in BrE, so in formal writing it is better to use 'many' or a 'large number of' in statements." https://www.italki.com/question/122661?hl=en-us
Людей is the genitive plural for человек(person). It is a lot OF people, so it is in the genitive. here's the declension of человек: https://cooljugator.com/run/%D1%87%D0%B5%D0%BB%D0%BE%D0%B2%D0%B5%D0%BA
I have issues with this sentence structure all across the set of Russian languages. It rarely works (I believe it does for "in the papace, there are guests" but NOT for "in the bag, there are groceries"), but it ought to be accepted.
I always prefer to think like a native speaker, and native Russian speakers use that order (I guess, if duolingo is at all accurate). If I can't recall a phrase, translating from English is a last resort - one thats 52,000x harder when you learn it in pedantic english word order.