I don't know about L-0, and i don't think it does exist in real life, but i do know about L-1, L-2, L-3, and L-4
L1- schedule comprise key events or major milestones selected as a result of coordination between client and contractor. It does represent in the format of list, summary schedule or in the form of Bar chart. Example of L-1 schedule activities, mobilisation of major equipment or installation of major equipment.
L2 -Schedule comprise of Critical network activities and other senior project management selected activities with mainly there ES and EF dates. L2 schedule provides integral plan of the Project activities for Project management.
L3- Schedule shows lowest level of details necessary to complete the project through Job Completion and also to finalize remaining requirements for the total project. example if L1 shows structural steel engineering activity/task then in L3 this particular activity likely to break up in more activities with shorter durations such as define and collect loads, drawing specifications etc.
L4- Schedule two to six week look ahead schedule that shows resources assigned, detailed and work activities and L4 schedule is mainly used planning and progress reporting purposes and advance planning for near term future week work