We report on the realization of an ultracold mixture of lithium atoms in the ground state and ytterbium atoms in an excited metastable (3P2) state. Such a mixture can support broad magnetic Feshbach resonances which may be utilized for the production of ultracold molecules with an electronic spin degree of freedom, as well as novel Efimov trimers. We investigate the interaction properties of the mixture in the presence of an external magnetic field and find an upper limit for the background interspecies two-body inelastic decay coefficient of K2'<3×10(-12) cm3/s for the 3P2 mJ=-1 substate. We calculate the dynamic polarizabilities of the Yb(3P2) magnetic substates for a range of wavelengths, and find good agreement with our measurements at 1064 nm. Our calculations also allow the identification of magic frequencies where Yb ground and metastable states are identically trapped and the determination of the interspecies van der Waals coefficients.