How to hide Box in Graphics3D?

This should work as you need to feed the option Boxed -> False to Graphics3D and option should be given after the argument in a function.

splot1 = SphericalPlot3D[
Cos[θ], {θ, 0, Pi}, {ϕ, 0, Pi}, Mesh -> None, 
PlotPoints -> 80];
aGraphicsComplex = splot1[[1]];
Graphics3D[{Lighting -> {{"Point", RGBColor[1, .9, .9], {2, 2, 4}}}, 
aGraphicsComplex /. 
GraphicsComplex[pts_, objs__] :> 
GraphicsComplex[
 With[{r = 4 Sin[11 (ArcTan[#[[1]], #[[2]]] + #[[3]])]}, {r, r, 
      2} #] & /@ pts, objs]}, Boxed -> False]

Boxed -> False is an option of Graphics3D so it must come after the first argument, not as part of it in a list.

Graphics3D[{...}, Boxed -> False]

This is valid for the other options too, just move them to the end.