Yes, most of the known multiscale or multirate decompositions, as long as they combine at one stage a non-ideal filter and a subsampling operator, induce some kind of aliasing at the analysis stage. And the Laplacian pyramid does so. But proper designs allow perfect reconstruction, so the aliasing can be reversed or cancelled, and kept reasonable in the case of processing between analysis and synthesis.
The simplest form of alias cancellation arises with Haar sum and difference filters. Consider $h_l = [1,1]$ and $h_h = [1,-1]$, the sum and difference filters, followed by a 2-fold downsampling. Both filters have very poor frequency responses, and cause aliasing with downsampling.
Take signal $X=[a,b]$. With the above scheme, you get two outputs $y_l = a+b$ and $y_h = b-a$, from which you can recover $X$ with $(y_l-y_h)/2 = a$ and $(y_l+y_h)/2 = b $. The latter operations are filtering by an averaged difference filter, and an averaging filter, e.g. the same as above, with a different scaling factor.
That is the magic of perfect reconstruction filter-banks: from well-chosen imperfect analysis filter-banks (with some decimation), to be able to design a synthesis filter-bank, itself imperfect, that cancels aliasing and distorsion of the whole analysis-synthesis system. It may happen as long as you have two or more channels, and with a little oversampling in the system, you can even find optimized inverse filter-banks.