CIELAB space was designed with the goal that any pair of colors separated by about 1 unit (i.e. ΔE = 1) would have a similar degree of apparent difference. However, apparent color differences are a highly non-linear property, and so by the point ΔE gets past 5 or 10, a specific color difference in one direction or one part of the color space will be substantially different than a same-distance color difference in another part of the space.
Often, the reason you want to carefully pick a color scheme is to make sure that two areas of a graphic are easily visually distinguishable along an edge. Because human vision mainly uses a monochromatic color signal for distinguishing shape, texture, and the finest details, the most important difference to make between a pair or set of colors is to separate them in the lightness (in CIELAB, that's L) dimension. If you have sufficient lightness contrast, then any particular choices of a and b (or hue and chroma) will work fine. If you don’t have sufficient lightness contrast, changing the other color components won’t help much: even if you maximally separate them in the color space, they’ll just appear to mush together in a clashing way along edges.
[edit: removed asterisks from L*, etc. because HN thinks they should be for italicizing]