Most of the time it will be a castor problem, but you need to get all the other worn parts(if any) replaced first. JDM suspension lifts as RMP&O pointed out have a history of half assed componentry and workmanship. In Japan, its all about the lift, not about the handling. In Western Australia when they were still importing them , the traffic branch would not lic them until they were returned to stock. At least the Japanese seem to have stopped using those 4 inch anodised pink or blue aluminium shackles
Its not uncommon, as I mentioned before about the castor, the suspension upgrade maybe ok when new. But as it sags with age and usage, the geometry changes and then you get death wobble. I had it on my my FJ73 (a shorter 2dr version of yours) about 5-6 years after I lifted it. The sag was barely noticeable. The shop had problems diagnosing it, so they made the castor worse to make the death wobble worse and then corrected it bit by bit . No problems after that. It is corrected with shims. My wobble was worst when towing