We report a self-accelerating wave packets eigenmode solution of a two-dimensional (2D) nonlocal nonlinear Schrödinger equation (NNLSE) with an Airy-beam time-dependence, and present their spatiotemporal profiles. The behaviours of such Airy-Laguerre-Gaussian light bullets, as propagated in a strongly nonlocal nonlinear medium (SNNM), are investigated both analytically and numerically. We found that the generation, control, and manipulation of the NL spatiotemporal light bullets are affected by the radial mode number and the azimuthal mode number, as well as the modulation depth. Our scheme is quite different from the linear light bullets, in which the wave propagates in a NL medium and is an eigenmode of NLSE.