Well, strictly speaking our means belonging to us and refers to more than one person; when speaking of more than one person, you are always speaking of more than one life.
Therefore "Laughter is an important part of our lives." is the correct version.
However if two people share a special bond (husband & wife, lovers, family members, etc.) I think it is possible for them to use the singular version to imply that their lives are closely related. Though I'm not 100% sure that I'm correct.
I am interested to see what others think of this.
A more general alternative is: laughter is an important part of life.
I'm not a teacher.