I do use the LRS plugin, but I don't see this functionality in that plugin. Thank you.
Unlike Arcmap you don't need a separate tool or even a plugin to access this information in QGIS (at last from version 3.4, maybe in earlier version as well).
By using the "identify features" tool you have access to all kind of geometric information in the "derived section" including closest vertex M value and interpolated M value.
Of course this work only on LineStringM geometry (or LineStringZM) with non null M value (or in other word in calibrated route).
Another way around this should be calculating length of line / route layers using field calculator such as this