how and why did Dr. Lanyon die?

Just after his irrepairable break with Jekyll, Lanyon fell ill. He died within days. We are not given the details of his illness. 

A week afterwards Dr. Lanyon took to his bed, and in something less than a fortnight he was dead.

Dr lanyon died because of seeing the transformation of Dr jekyll into Mr Hyde.Lanyon is the only person to see Hyde actually transforming into jekyll.Something that does not fit the laws of science.When sees the change he cannot cope with the fight between his common sene view of the world and what jekylls experiments reveal "I ask myself if I believe it ,and i cannot answer.My life is shaken to its roots ".Not long after he becomes mentally and physically ill,and dies.

Dr.Lanyon is the first one who sees the transformation. As he sees the trasformation he is aghast by it. Later when Jekyll tells him everything he is shocked to hear that life has horrors too for his life has always been pleassent. he says so. A week later he dies of the shock

Because he becomes traumatised at the sight of Hyde turning into Jekyll.

lanyon died because lanyon chose to witness Mr.Hyde turn into Dr.Jekyll.When Lanyon saw that he got really scared and got ill form it and died by the illness