The following list is by no means complete, it includes just "Best Director" and "Best Film" nominations and wins.
Lasse's movies have won a lot more awards, you can see them all in detail in the movie vault.

1986

New York Film Critics Circle

My Life as a dog

won for Best Foreign Film

1987

Academy Awards	My Life as a dog	nominated for Best Director nominated for Best Screenplay Based On Material From Another Medium
Directors Guild Awards	My Life as a dog	nominated for Outstanding Directorial Achievement in Motion Pictures
Bodil Awards	My Life as a dog	won for Best European Film
Robert Film Festival	My Life as a dog	won for Best Foreign Film

1988

BAFTA Awards	My Life as a dog	nominated for Best Foreign Language Film
Independent Spirit Awards	My Life as a dog	won for Best Foreign Film

1995

Guild Film Awards

What's Eating Gilbert Grape

won silver for Best Foreign Film

1999

Venice Film Festival

The Cider House Rules

nominated for Best Film

2000

Academy Awards

The Cider House Rules

nominated for Best Director

2001

Berlinale	Chocolat	nominated for the Golden Berlin Bear
Bodil Awards	The Cider House Rules	nominated for Best American Film
European Film Awards	Chocolat	nominated for Best Director
Guild Film Awards	Chocolat	won gold for Best Foreign Film
Palm Springs International Film Festival	Chocolat	won the audience award

2002

Berlinale	The Shipping News	nominated for the Golden Berlin Bear
Goya Awards	Chocolat	nominated for Best Foreign Film