Chebyshev-like bias conjecture for entry points of primes in Lucas sequences

Let $U$ be a Lucas sequence with discriminant $D$, and let $z_U(p)$ be the entry point of a prime $p$ in $U$, with $z_U(p)=\infty$ for primes dividing $Q$ but not $P$. Define

$$R_U=\left\{p\in\mathbb{P}:\left(\frac{D}{p}\right)=1\right\},\qquad N_U=\left\{p\in\mathbb{P}:\left(\frac{D}{p}\right)=-1\right\}.$$

For $x>0$, set $Z_U(x)=\{p\in\mathbb{P}:z_U(p)\leq x\}$, $Z_U^R(x)=Z_U(x)\cap R_U$, and $Z_U^N(x)=Z_U(x)\cap N_U$, and define

$$B_U(x)=\#\left\{1\leq n\leq x:\#Z_U^N(n)<\#Z_U^R(n)\right\}.$$

Chebyshev-like bias conjecture. (Weak) If $U$ is a regular Lucas sequence with $D>0$, then

$$\frac{B_U(x)}{x}\underset{x\rightarrow\infty}{\longrightarrow}1.$$

(Strong) If $U$ is a regular Lucas sequence with $D>0$, then $\#Z_U^N(n)<\#Z_U^R(n)$ for all but finitely many $n\geq1$; in particular, for the Fibonacci sequence $F$,

$$\#Z_F^N(n)<\#Z_F^R(n)$$

for all $n>36$. This conjectures a strong Chebyshev-like bias favoring primes with Legendre symbol $\left(\frac{D}{p}\right)=1$ among the entry points of primes in real regular Lucas sequences. The weak and strong forms remain open in the supplied text.