'A lot' is used to quantify all types of nouns both countable and uncountable. 'A lot of friends', 'a lot of water.' and describes an unspecific large quantity. It is also used as an adverb to denote the degree or extent of something. He loved her 'a lot'.
Much is used a) to quantify uncountable nouns: much affection, not much money. b) as an adverb to denote the degree or extent of something. She's much better now, He was 'much' annoyed (here 'much' means the same as 'very' you can say he was 'very' annoyed). To make it stronger you can put 'much' and 'very' together 'He was very much in love.'
'Very' is an intensifier and can be used with some adjectives to make them stronger 'very happy.' or with much and many to make them stronger.