Long-lived high-K states have been identified in 177Lu, including an isomer with τ>10 μs, placed at 3530 keV and associated with the yrast Kπ=39/2−, 5-quasiparticle state predicted in multi-quasiparticle-state calculations. The γ-decay of the isomer exposes the rotational band based on the 160-day 23/2− isomer, , with band properties which support its proposed configuration. A 90-ns isomer at 1325 keV is associated with the predicted 3-quasiparticle Kπ=25/2+ state while a 5-quasiparticle 33/2+, 902-ns isomer with highly-hindered decays is identified at 2771 keV. Both exhibit rotational bands whose properties are used to support the assigned configurations. The possibility that the Kπ=39/2− isomer found in this work should be identified with a β-decaying isomer, proposed recently to populate the 51-min 37/2− isomer in 177Hf, is discussed in terms of the implied logft values, configuration changes, and hindrances for K-forbidden γ-decays.