While the underlying concept for lactate threshold is the workload at which lactate can not be cleared as fast as it's produced, there are at least several dozen specific definitions of LT. These include a 1 mmol/l rise above baseline, 2 mmol/l above baseline, 2.5 mmol/l above baseline, 4 mmol/l absolute, etc. where baseline may be defined in terms of lactate concentration at rest or during light exercise. Not to mention the myriad ways to define the change in slope you refer to. Any report of LT values has to state precisely how LT is measured. So to say there is a single definition is truly misleading.

As to your examples with gear and cadence, the only protocols I trust to determine LT are independent of gearing. Using an ergometer, power is controlled and the rider is free to self-select the best cadence for them, because power is controlled independent of wheel speed, gearing is not a factor. Artificially imposing cadence or gear restrictions means that someone is no longer measuring LT, but something related to LT but confounded by the artificially imposed constraints.