The M105 comes from host temperature answers, these are always there so ignore that.
LCD is independent of eeprom values at least meaning that you see it. Some Arduino Due clones have a bug that they do not start properly first time they get power and only after a reset you see everything. But if you connect with host it with programming port it will reset (not on native port).
M502 / M500 overwrite eeprom with config values. So that deletes your old settings. So what do you get when you say lost?