I would say
she has got a lot of things /lots of things to do.
Normally, especially in written English, a lot of and lots are both used in affirmative sentences, whereas much and many are to be found in negative sentences or in question forms, e.g.:
Has she got much to do?/ Has she got many books at home??
She hasn't got much to do./ She hasn't got many books at home
She has got lots to do/ She has got a lot of books/lots of books at home.
I hope this will help a little.
Student or Learner