EDIT: This is a major revision in light of sources provided by @ErickWong's comment.
The summatory Liouville function (OEIS sequence A002819) is $$L(n)=\sum_{1\le k\le n}(-1)^{\Omega(k)}\quad (n=1,2,3,\ldots)$$ where $\Omega(k)$ is the number of prime factors of $k$ counted with multiplicity. Thus $L(n)$ is the sum of the "parities" ($+1$ if even, $-1$ if odd) of the first $n$ values of $\Omega.$
Here is a plot of the first $10^9$ values of $L$, including overlays of some approximating curves:
The overlays are as follows:
A "central" curve (gray) ${\sqrt{n}\over\zeta({1\over 2})}$ whose functional form is suggested by Tanaka's 1980 proof (mentioned here and proved here) that $\ L(n)-{\sqrt{n}\over\zeta({1\over 2})}\ $ changes sign infinitely often as $n\to\infty.$
A "sinusoid" (red) which oscillates about the central curve with increasing "wavelength" and amplitude: $$\hat{L}(n) = {\sqrt{n}\over\zeta({1\over 2})}\left( 1 + \sqrt{1\over 2}\,\sin\left(t_1\ln(n) + 2.75\right) \right) $$ where $\zeta$ is the Riemann zeta function and $t_1$ is the imaginary part of the first nontrivial zero of $\zeta$. Thus $\zeta({1\over 2})=-0.684765236\ldots$ and $t_1=14.1347251\dots.$ The occurrence of $t_1$ in the argument of the sine function is suggested by the "summary description" of a Wikipedia plot here. I've adjusted the parameters of the sinusoid, including amplitude and phase, to obtain a visual fit.
Q1: The mentioned "summary description" cites this paper ("On Differences of Zeta Values"), which proves an asymptotically oscillatory behavior of the coefficients in a certain series representation of Riemann zeta. How does this lead to a zero of Riemann zeta appearing in $\hat{L}?$
Q2: Can it be shown that regular oscillatory behavior of $L(n)$ persists for arbitrarily large $n$?
NB: This behavior says nothing about how often $L(n)>0$ may occur (such as the "spike" in the plot at $n\approx 9\cdot 10^8$); i.e., it may be independent of whether $L$ changes sign infinitely often.