Let $Q(u,v)$ be a positive definite binary quadratic form with arbitrary real coefficients. For large real $x$, one may ask for the number $B\left(x\right)$ of primitive lattice points (integer points $(m,n)$ with $gcd(M,n)=1$) in the ellipse disc $Q(u,v)\le x$, in particular, for the remainder term $R\left(x\right)$ in the asymptotics for $B\left(x\right)$. While upper bounds for $R\left(x\right)$ depend on zero-free regions of the zeta-function, and thus, in most published results, on the Riemann Hypothesis, the present paper deals with a lower estimate. It is proved that the absolute value or...