Atom interferometry deploys atoms as sensors, delivering precision measurements that span the gamut of physics. Laser-cooled samples simplify uniform detection strategies and allow meticulous control over degrees of freedom and systematic effects. Advanced cooling and interferometry techniques do apply readily to a few atomic species, but they leave behind a large class of species otherwise suited for precision sensing. This thesis describes atom interferometry with a sample of lukewarm $^7$Li, near the Doppler temperature. High thermal speeds demand rapid atom optics and complicate detection. We nevertheless develop interferometer techniques that considerably relax cooling requirements, including a recoil-sensitive scheme capable of measuring the fine-structure constant that takes advantage of $^7$Li's low mass. We also establish a phase-patterning protocol to inscribe and sense spatially-varying phases with matter-wave interferometers whose sample sizes exceed the arm separation. Phase patterning forms the basis of the first precision measurement of $^7$Li's red tune-out wavelength, the wavelength where AC Stark shifts from the $D$-line transitions cancel and the polarizability vanishes. Our measurement registers a 3-$\sigma$ tension with \emph{ab initio} atomic theory regarding the tensor-shifted tune-out wavelength and a 2-$\sigma$ tension regarding the size of the tensor shift, but agrees with theory regarding the scalar tune-out wavelength. These results motivate further work on lithium's polarizability, enable direct measurements of hyperpolarizability, and empower an assortment of future applications of phase patterning in matter-wave interferometry.