To go lickety-split means to rush headlong towards something, or travel at full speed. To me, it rather suggests one should be heading in the direction of a couple of frightfully nice chaps, serving lashings of ginger beer.
We don't generally go lickety-split in our van (it doesn't half rattle if we do) but we expect it to go where we want when we want. The other day it wouldn't go anywhere. Fortunately the RAC where able to coax it back into action.
We visited this castle with our van. I climbed the first turn of steps lickety-split, but by the time I reached the top it was more ... well what word or phrase do you think sums up the red-faced, gasping mess I was when I got up there?