This has been bothering me for a while. I have been convinced that such examples exist but cannot come up with one.
Basically I have been playing with different posets, for eg elements arranged as nodes in a hexagon (https://en.m.wikipedia.org/wiki/Lattice_(order)#Counter-examples) similar to the counter example here. But cannot figure it out exactly.
Any help and pointers would be great.
I suppose that by CPO you mean a Complete partial order, which some define as a poset in which every directed set has a supremum (this is the first definition in the linked Wikipedia article).
Since every finite poset is directed-complete (see first example in linked page), it is enough to take a finite poset with top element (and bottom, if you will) that is not a lattice.
By the way, one concrete example is the pic. 7 in your linked page.