Extreme continuum variability in extragalactic nuclear sources can indicate extreme changes in accretion flows onto supermassive black holes. We explore the multiwavelength nature of a continuum flare in the Seyfert LCRS B040659.9$-$385922. The all-sky X-ray surveys conducted by the Spectrum Roentgen Gamma (SRG)/extended ROentgen Survey with an Imaging Telescope Array (eROSITA) showed that its X-ray flux increased by a factor of roughly five over six months, and concurrent optical photometric monitoring with the Asteroid Terrestrial-impact Last Alert System (ATLAS) showed a simultaneous increase. We complemented the eROSITA and ATLAS data by triggering a multiwavelength follow-up monitoring program (X-ray Multi-Mirror Mission: XMM-Newton Neutron star Interior Composition Explorer: NICER; optical spectroscopy) to study the evolution of the accretion disk, broad-line region, and X-ray corona. During the campaign, X-ray and optical continuum flux subsided over roughly six months. Our campaign includes two XMM-Newton observations, one taken near the peak of this flare and the other taken when the flare had subsided. The soft X-ray excess in both XMM-Newton observations was power law-like (distinctly nonthermal). Using a simple power law, we observed that the photon index of the soft excess varies from a steep value of $ 2.7$ at the flare peak to a relatively flatter value of $ 2.2$ as the flare subsided. We successfully modeled the broadband optical/UV/X-ray spectral energy distribution at both the flare peak and post-flare times with the AGNSED model, incorporating thermal disk emission into the optical/UV and warm thermal Comptonization in the soft X-rays. The accretion rate falls by roughly 2.5, and the radius of the hot Comptonizing region increases from the flaring state to the post-flare state. Additionally, from the optical spectral observations, we find that the broad He ii lambda 4686 emission line fades significantly as the optical/UV/X-ray continuum fades, which could indicate a substantial flare of disk emission above 54 eV. We also observed a redshifted broad component in the H$ beta $ emission line that is present during the high flux state of the source and disappears in subsequent observations. A sudden strong increase in the local accretion rate in this source manifested itself via an increase in accretion disk emission and in thermal Comptonized emission in the soft X-rays, which subsequently faded. The redshifted broad Balmer component could be associated with a transient kinematic component distinct from that comprising the rest of the broad-line region.