We report here on a unique, newly discovered, silica-rich ungrouped achondrite Northwest Africa 11575 (NWA 11575). NWA 11575 is one of four known silica-rich ungrouped achondrites, presenting evidence for igneous processes resulting in evolved compositions early in the history of the solar system. It is unique from the other silica-rich ungrouped achondrites in that it has pyroxene compositional trends matching those of lunar samples and martian meteorites; contains quartz and potassium feldspar; and contains oxygen, hydrogen, and chromium isotopes that are similar to those of LL chondrites. Together, these four silica-rich ungrouped achondrites provide evidence for evolved compositions resulting from igneous processes on at least three separate bodies. NWA 11575 consists of two lithologies, the host or light lithology and the dark lithology. The dark lithology occurs as clasts within the light lithology, with a distinct contact between the lithologies. The mineralogy of the host lithology consists of 53.8% oligoclase, 34.1% pyroxene, 4.8% potassium feldspar, 3.8% quartz, and 2.6% apatite and merrillite, along with minor chromite, ilmenite, iron oxide, iron sulfide, and low-Ni iron. The apatite is three times more abundant than the merrillite. The dark lithology consists of 70% groundmass and 30% pyroxenes but has a similar trachyandesitic to andesitic bulk composition. Apatite is present in some regions within the dark lithology but is not ubiquitous. The pyroxene compositional zoning trend for the light lithology consists of magnesian pigeonite, mantled by an augitic layer, and then rimmed by ferropigeonite. Numerous similarities between the host and dark lithologies, such as similar oxygen isotopic compositions, bulk compositions, and pyroxene trends, suggest that the host and dark lithology are derived from the same source, but differ in their cooling and crystallization histories. One possible interpretation is that the host and dark lithologies are lavas formed through extensive magmatic differentiation, possibly derived from a precursor of chondritic composition, which erupted on the surface of their parent body. The dark lithology cooled quickly forming a quenched glass with hopper pyroxenes. The later-erupted material, perhaps with more overlying material to insulate the magma and provide for a slower cooling rate, cooled slowly enough to crystallize complexly zoned pyroxenes, feldspars, and a residual mesostasis of quartz, potassium feldspar, apatite, and minor phases. Alternatively, the dark lithology could be an impact melt. Either process could have occurred on a volcanic parent body with oxygen isotopes similar to those of LL chondrites, or at some location on the LL-chondrite parent body itself.