These phrases are roughly equivalent. 'Lots of' is a bit more informal than 'a lot of'. 'Plenty of' may imply sufficiency in addition to quantity. One useful trick is that many nouns in English require either 'much' or 'many', but are incorrect if mismatched e.g., 'much milk' and 'many cows' -- however, you can say 'lots of cows' and 'lots of milk', and both phrases are correct. For anyone interested in differences between written and spoken English: Be aware that a verb will usually (in conversation, at least) take the number of the items: "There are a lot of cows." "There is a lot of milk." and in informal conversation it is also common to hear "*There's/There're lots of cows." "There's lots of milk." -- both of these would be found in quotations of everyday speech but are not necessarily considered correct when written.