Lithium AAAA is news to me. No word yet on whether anyone will build lithium AAA. Several forumites have asked Energizer quite a number of times, I think.
When you are just generally comparing lithium cells to alkalines, you will have greater leak resistance, longer shelf life, higher power capacity for equivalent size (higher power density), lighter weight, ability to deliver higher currents without excessive drop in operating life, ie with alkalines, they may be rated 2800mAh, but you could only draw that much power if you ran it approx. 10mA. If you started to run 500mA, you will probably get only two thirds of the capacity, the rest going to waste in internal resistance and heating up the cell.
The thing about brighter output between AA lithiums and alkalines is because the lithiums usually start out at 1.7V nominal, whereas the alkalines would be around 1.5V. Also, since lithiums have lower internal resistance, high drain applications, like incandescent bulbs, will be able to draw the necessary current without difficulty, resulting in a brighter light. An alkaline may start to experience losses due to internal resistance and so may not be able to supply all the necessary current. That is also why, in high-drain applications, AA lithiums will perform better. But in terms of power capacity of AA lithiums verses AA alkalines, they are quite similar, so you would probably not see any benefits using lithiums in low-drain applications.