Lost Nuetral - Turning Lights On Stops Others Flickering
With a neutral, everything is forced to be split 50/50, regardless of load. When you have a lost neutral, your circuits that are normally ~ 120V can be anywhere between 0 V and 240 V.  The voltage on each side will float depending on the relative load of each side. Add more load and things could even out.
Some devices won't work well outside a narrow range - perhaps 100 V - 130 V. Many devices can handle a wide range for internationalization - e.g., 90 V - 250 V. But go too low, especially below 90 V, and a lot of devices simply won't work properly. Flickering lights would be the least of the problems. LED lights in particular will flicker if voltage is too low, unless (and sometimes even if) they are designed to be dimmer-compatible.