  Boij-S\"oderberg theory describes the scalar multiples of Betti diagrams of
graded modules over a polynomial ring as a linear combination of pure diagrams
with positive coefficients. There are a few results that describe
Boij-S\"oderberg decompositions explicitly. In this paper, we focus on the
Betti diagrams of lex-segment ideals and describe the Boij-S\"oderberg
decomposition of a lex-segment ideal in terms of Boij-S\"oderberg
decompositions of some other related lex-segment ideals.
