I don't know the name of the wiring style, but if the live feed goes to the next light via the fitting which has been removed then there is every chance that wiring it back correctly will fix the problem.
In the mean time I would not recommend having the lighting circuit switched on as it sounds like there may be a live wire left somewhere within the removed fitting.
Taking down one light fitting has in effect broken the electrical feed to the rest of the lights on that circuit. Yes if you replace the light fitting and connect it up exactly as it was all other lights should then work, but remember to switch off at the fuseboard first!!
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