Why is it not lattice?
its a lattice.
Lattice : A poset (L , ≤) is a Lattice iff for all a , b ∈ L LUB(a,b) and GLB(a,b) both exist and ∊ L
A lattice must be first a poset i.e. it should be reflexive , anti-symmetric and transitive.
Here b ≤ c & c ≤ b so, it is not antisymmetric & hence not a lattice.
X->YZ , Y->XZ , ...