According to the Toyota factory maintenance schedule, an automatic transmission fluid change is not required for the Rav4 under normal operating conditions, hence the "lifetime fluid" assumption. Same thing with Volkswagens, although with VW's they also say you don't need to check it regularly either.
However, Toyota recommends a fluid change every 60K miles if your Rav4 fits the "special operating conditions" description. The maintenance items that used to be considered normal maintenance are now considered "special operating conditions" items. It's a load of crap. For all practical purposes you should consider your Rav4 to be in "special operating conditions" and perform the associated maintenace if you want it to last a long time.
Manufacturers these days have extended or eliminated transmission service intervals, not because the transmission design or fluid technolgy has advanced, but because consumers and the government have demanded that cars require less maintenance. I believe that extended intervals is one of the factors that caused the famous Toyota engine sludge problem. Honestly, automatic transmissions have not changed a whole lot in the past 50 years, so service intervals should not change.
Keep in mind that a transmission fluid "change" is different than a "flush". When someone peforms a "change", they just drain the fluid out of the tranny pan, and maybe clean the filter. Due to the design of the transmission, that method only actually drains 1/3 of the fluid, and leaves the other 2/3 in the torque converter and tranny cooler lines. When someone performs a true "flush", they hook up a machine to the transmission which pumps out all the old fluid and pumps in new fluid. This is the preferred method because it replaces all of the fluid. However it really boils down to personal preference.
I have a manual transmission, but I change the gear oil every 30K miles. If I had an automatic, I would get it "flushed" every 60K miles. Some people will do a drain and fill, or "change", every 20K-30K miles, but I think a real "flush" every 60K is better because I tend to be hard on my transmissions. In any case I would let only a Toyota dealer perform a tranny service (if I didn't do it myself) because the Rav4 can be picky, and they have all the right fluids and specs.
As for the fluid, the 2001 Ravs require genuine Toyota Type-IV ATF, and if you use anything else it will screw up the transmission.
If I were you, I would call up the Toyota dealer and ask them what they recommend for the tranny service on the Rav. Each dealer has their own schedules and services they offer. My local Toyota dealer recommends ATF changes every 30K miles, but that's mainly just to make money. Toyota itself says you only need to do a "change", and that's only "as necessary", but if your dealer says they can do a real flush, then go for it at 60K miles. Otherwise just do the regular "change" as soon as you can do it. After all, extra money spent now will help prevent a tranny disaster down the line.
I'm sure some of you will disagree with me, but that's just my opinion which is based on information I've gotten from trusted mechanics I know. I also tend to be overzealous with maintenance, so in reality you should be fine just getting a standard ATF change every 30K miles. The decision on whether to drain/fill or flush the ATF fluid is subject to the same debate as premium gas or synthetic oil; everyone has their own opinion, and there is a lot of misinformation (or rumors) floating around.