In lang=en terms the difference between madrigal and lied
is that madrigal is a polyphonic song for about six voices, from 16th century Italy while lied is an art song, sung in German and accompanied on the piano.
As a verb lied is
past tense of lie.
madrigal
Noun
(
en noun)
(music) a song for a small number of unaccompanied voices; from 13th century Italy
(music) a polyphonic song for about six voices, from 16th century Italy
a short poem, often pastoral, and suitable to be set to music
lied
English
Etymology 1
Noun
(
wikipedia lied)
(
lieder)
(music) An art song, sung in German and accompanied on the piano
Etymology 2
From (etyl) .
Verb
(head)
(lie)