You are probably right, it is an issue with color profiles and gamut. Aperture does use a different raw converter, which will create some variance. In fact, many like the look of straight Aperture raw conversions over straight ACR conversions. But if the washed out look is dramatic, and Photoshop opens your raw files okay, then it must be a profile issue.
It may help to explain how you are exporting from Aperture. Are your source files raw files, PSDs, TIFFs, or JPEGs? Are you exporting masters, or are you exporting versions? If you're exporting versions, take a look at your "source preset" when exporting. What color profile are you embedding?
Although if you are embedding any color profile, Photoshop and Lightroom should pick it up.
All I've read is that Lightroom manages profiles more transparently than Photoshop, but perhaps someone could jump in here and say how it is managed.
Finally, what purpose are you exporting and importing into Lightroom? If you're migrating your library to a Lightroom catalog, you may be best served by using the Aperture migration plug-in.
Aperture import plugin now available
The plug-in still has issues with foreign characters, importing all previews, and face keywording and keywording previews. You'll be better off waiting until these issues are fixed. Even if you can't, the plug-in would still be a better option than a manual attempt, unless you're doing something other than migrating your Aperture library.