The muon spin relaxation technique has been used to study spinet lithium manganate insertion compounds. Two spinet compositions of lithium manganese oxide have been studied: mixed valence (Mn-III/Mn-IV) LiMn2O4, where the lithium extraction process is mainly by redox. reaction, and Li1.33Mn1.67O4, where all the manganese is Mn-IV and lithium extraction is a lithium by proton ion exchange. Extraction of lithium from the former gives a spinet manganese oxide without lithium or protons (lambda-MnO2), while from the latter a protonated manganese oxide is obtained (H+-MnO2). Muons are quasi-static in these compounds, and they are located both in "regular" lithium and proton sites and in interstitial sites of the spinet structure, these latter being used during diffusion of lithium ions and protons. Results clearly reflect the presence of protons in H+-MnO2 and the movement of lithium ions in both lithium manganates. The lithium-rich phase Li1.33Mn1.67O4 is characterized by an increase of the number of implanted muons localized in interstitial sites, as well as by a decrease of the onset temperature for lithium diffusion.