If I've been walking a Lapras for a while and currently have, say, 4.5km out of the required 5km to get my next candy, what happens when the event that reduces the distance to 1/4? Will I have to finish that 5km before I have the reduced rate?
It's actually very beneficial to be close to earning your next buddy candy when an event like this starts, because you'll be given candy for distance covered before the event actually started.
When the event starts and lowers the required buddy distances, the overflowed distance you've already walked will cause you to be immediately rewarded with candy for the progress you've made towards the new distance.
For instance, if you've walked a Lapras 4.5/5km, you'll receive 3 candy as soon as the event starts and Lapras will be at 0.75/1.25km for its next candy.
Thus, the best way to use this event is to stop accruing walking distance as close to your next reward as possible, so you'll get 3 free candies!