It would be difficult for a definition to make any presuppositions. You could have a definition that defines some set in which a contradiction is involved ("an integer is special if it is both prime and divisible by 4"), but then you'd say that the set so defined is empty, not that the definition is incoherent.

It is quite common for a lemma to be needed to ensure that a definition is well-defined. The term “defi-lemma” exists for a reason.

As a simple example, suppose X is a set and r is a relation on X. If I define Y := X/r , the set of equivalence relations with respect to r, this implicitly assumes that the relation r is an equivalence relation.