Yes you would be in economy if only L is available. You can waitlist for the higher booking class in accordance with fare rules, but there is no guarantee it will clear even if the cabin is not full.

If you change LHR from a transit to a stopover be aware that taxes will go up substantially (currently 80 pounds and will be going up further from November). Depending on airline you might or might not be able to through check bags NRT-LHR-LIS across separate tickets, and probably won't be able to check in for LHR-LIS until you reach LHR.

Yes, if you misconnect on separate tickets it is up to the goodwill of the airlines as to how they handle it. In practice as long as you have status and/or high fare you will get rebooked, but depending on availability it might not be same day.