Let

$V$ be an Euclidean Jordan algebra,

$K$ be a symmetric cone in

$V$,

$L:V\u27f6V$ be a linear transformation and

$q\in V$. The linear complementary problem associated to

$L$ and

$q$,

$\text{LCP}(L,q)$, prescribes finding

$x\in V$ such that

$x\in K$,

$Lx+q\in K$ and

$\langle x,Lx+q\rangle =0$. It is well known that when

$V={\mathbb{R}}^{n}$ and

$L$ is a real matrix,

$\text{LCP}(L,q)$ has a unique solution for all

$q\in {\mathbb{R}}^{n}$, iff all the principal minors of

$L$ are positive. In this case the solution map of the

$\text{LCP}(L,q)$ is well defined and Lipschitz continuous in

${\mathbb{R}}^{n}$. The main result of this paper establishes one direction of the analogous property in the general case: if the solution map is Lipschitz continuous and if

$L$ has the

$Q$-property, then

$L$ has the positive principal minor property.