Evolution of the combined ϵ CMa and β CMa Strömgren sphere (dotted orange ring), the Local Bubble (“LB,” purple ring), the CLIC (average trajectory shown in red), and the Sun (trajectory shown in yellow). The Local Bubble at t < 0 Myr is modeled as an idealized, expanding spherical shell (C. Zucker et al. 2022), with the more structured, nonspherical boundary constrained by the present-day 3D dust distribution (T. J. O’Neill et al. 2024b) shown at t = 0 Myr. Under the strong assumption of a constant electron density, the Local Bubble was born within and has partially overlapped with the boundary of a Strömgren sphere over its lifetime. Tracing back its present-day trajectory far beyond its presumed lifetime, we find that the CLIC has been traveling within the combined β CMa and ϵ CMa Strömgren sphere for the past several million years, whose trajectory is nearly perpendicular to the trajectory of the CLIC. The combination of the CLIC’s position interior to the Strömgren sphere and its motion transverse to the CLIC disfavors an origin for the CLIC tied solely to this prominent nearby Strömgren sphere.