The spin alignment of inelastically excited 7Li projectiles, when the target remains in its ground state, was determined through angular-correlation measurements between the breakup fragments of 7Li_ (_ + t). It was found that 7Li_ is largely aligned along the beam axis (longitudinal) in this type of inelastic reaction, regardless of the target. This longitudinal alignment is well described by DWBA calculations, which can be explained by an angular-momentum-excitation-energy mismatch condition. These calculations also explain the longitudinal spin alignment of excited nuclei in several other systems, showing the phenomenon is more general. The experiment involving 7Li was performed at the Texas A&M Cyclotron Institute, and used a custom designed detector system consisting of two annular Si-CsI(Tl) telescope arrays