An interesting question, some of us have pondered.
Here's a rather long-winded interpretation:
To date no one has come up with a printed factory production output for the complete run of the FJ4X series, or one that is split-out into individual models. I would suspect that data is closed-information within the Toyota Corporation. That is why the question resurfaces periodically about the pickups, the Troopies, the 1983 US imports of the FJ40, the number of wagons built, etc.. From a collector's standpoint, I can see this as being of value, especially as existing examples dwindle and values continue to escalate. And most of us simply would "just like to know." Various numbers are thrown-around out there, but hard data is in short supply.
I have never seen any numbers that separated-out the LWB(pickups) from the Troopies, or from the earlier 45V and 45LV, and SWB models. The 1986 factory Production Frame Reference shows three different and concurrent FJ45 serial numbering lines.
As discussed some years ago, there apparently was a need for a separate numbering system in the EEC(European market), perhaps somewhat similar to the decision to run concurrent but different numbering systems once the international VIN 17-digit system kicked in. Not every country immediately subscribed to the VIN numbering system, and Toyota itself in many markets was slow in so doing.
Anyway, factory records from January 1980-June 1986 show one line(the line most of us have seen examples of) beginning FJ45-249198 - FJ45-421310, another line FJ45-800082 - FJ45-810199, and a third FJ45-850001 - FJ45-850558.
A Russian website many years ago published serial numbers for the 45s starting from August 1978 with FJ45-0199119 which meshes correctly with the Factory lists above. They did not list their source of information.
The above lists do not include the BJ45 series, or the earlier 45 series from the 1960s. The earlier series has been documented by SpecterOffRoad, and is likely reliable considering their special relationship with Toyota, but not sure their numbers split-out the LWB from the wagons or the SWB. That listing starts in January 1964 with FJ45-15938 through November 1968 with FJ45-36802..
I have not seen any documentation of the numbers from December 1968-July 1978. An educated guess would be that the most common line that started back in the early 1960s and continued until the end, June 1986, would account for the "lost" numbers, perhaps as many as 180,000 units. These year variants never appeared in the USA at the time, so likely they continued in heavy demand in the Rest of the World(ROW).
One of the questions would be: did the FJ45 frame number system start with serial number 000001, or like some manufacturers in Europe, start with a much higher number for the very first produced?
And, as there are 15,000 unaccounted-for serial numbers preceding the Specter list--were there 15,000 trucks built before 1964, when only 4,000 or so were being produced yearly through the early 1960s? At that extrapolated rate, series production would have had to start somewhere around 1960?
Because we in the USA didn't continue to see importation of the 45s beyond 1967, we never saw the increased demand worldwide for these trucks for the next twenty years. What may seem "rare" to us, may be very "common" in other far-reaching corners of the world.
So............my "guess" FWIW, and this is my own interpretation, subject to more knowledgeable correction, would be a total of all 45s manufactured to be somewhere in the 500,000 - 600,000 range. How that splits-out into LWBs versus any others is unknown. It seems logical that from a worldwide utilitarian perspective, pickup trucks would have more value/use in second- and third-world countries than wagons or Troopies. How many have been used, abused, and destroyed over the years is also unknown--but likely a very high number from the looks of the bashed ones still remaining.
So, another somewhat related question surfaces as to how many of those vehicles are still "on the road" today. Which is why we see efforts made to document existing serial numbers. But sadly, voluntary reporting has limited results, whether it's for frame numbers or engine serials, etc..
While FJ4X, or simply J4X, vehicles are certainly "no Ferrari," it is natural for collectors, as well as insurers, to wrap their heads around a number--the number actually produced, and the number still left. When you explore the world of exotic and rare collector automobiles, this question of numbers becomes a big part of the equation of ownership, demand, and value.
It would be nice if someday, a kindly Japanese gentleman, once a Toyota executive "in the know," would share some numbers with all of us. Until then, it's really anyone's guess as to the answer to your question.
Perhaps the more frequency this question comes up, we will get closer to a more-firm determination.
Anyway, that's how I look at it.