Adobe does have an Aperture importer for Lightroom which will help you migrate everything.
If you allowed Aperture to manager your masters then they are all stored by year/month/day of shooting (they are organized by time within the library). If you manage your own masters then they could be stored anywhere (Aperture's library only keeps track of where the master is found on your filesystem. Although Aperture also allows for managing "offline" images as well (Aperture does a better job managing image masters than Lightroom... Adobe is a little sloppy.)
Whereas Aperture had a concept of "Projects", the Lightroom equivalent are called "Collections". It can convert your Projects into Collections for you. But you can create Projects/Collections based on anything (they are arbitrary albums of images that you assemble... based on any rationale you want (or no rationale at all). I have projects/collections based on subjects, based on favorite shooting locations, sometimes based on significant events, etc.)
I have no idea how Apple works the magic... but if you move the master images on the Mac filesystem using Finder (not using Aperture), somehow Aperture's library always knew that it was moved. IMPORTANT: if you do this in Lightroom... you'll screw up it's library. Any moving around of the masters MUST be done using that internal Library manager tool within Lightroom itself... you must NOT move images using Finder to reorganize things.
Once everything is imported, you'll have a large collection called "From Aperture" and within that you'll find a sub-collection for each Aperture Project you had.
However at the same time... it'll also copy over the masters (and it will "copy" them... it won't "move" them ... so make sure you have enough disk space). These will get copied into the folder hierarchy (not to be confused with collections) and these will be in folders based on year/month/day of shooting.
SO.... if you go into the folder view for each year/month/day and scan through, you'd likely see two side-by-side duplicates if you had already imported the image before (because they'll be sorted based on time of shooting.)
One more thing...
Aperture's importer knows how to find and copy over all the "masters"... but Aperture doesn't edit masters... a "version" of an image is based on (a) the original "master" is the baseline and then (b) all the adjustments are basically a list of meta-data and these are rapidly applied ONLY to the image you see on screen. There is no stored file on disk that has all the adjustments applied (the same is true of Lightroom). It only applies adjustments if you "export" the image (e.g. for printing, displaying on the web, etc. but the internal library doesn't contain a fully-adjusted copy of the image itself.)
This is important to remember BECAUSE when you do the import... every adjustment you ever made to the image in Aperture is NOT going to come over into Lightroom. What you'll have is a bunch of unadjusted images and you have to start from scratch and re-adjust them.
This wasn't a deal-killer for me since I do adjustments more as an "on demand" process (if I want to use an image, I'll adjust it. I'm not going to go through every image I imported and re-adjust it whether or not I ever plan to use that image.)