Geordie Williamson has found counterexamples to Lusztig's conjecture:
http://people.mpim-bonn.mpg.de/geordie/Torsion.pdf
Apparently, any bound on the largest prime that breaks Lusztig's conjecture must be at least proportional to $nlog n$, and this is probably still far too optimistic; I think it's now believed that you'll need an exponential bound.
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