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"by lot" is correct and usable in written English.
You can use it when referring to a process that involves objects being chosen randomly. For example, "The winner of the competition was selected by lot."
Exact(59)
They chose a name by lot.
The assignments to provinces were done by lot.
A man chosen by lot was not obliged to serve.
That sell-through rate 96% by lot, 98% by value hadn't been seen since 2004.
In most cases they were either voluntary victims or chosen by lot from among the devotees.
Ten judges of the Games were chosen by lot in Elis.
The dicasts were selected by lot, every citizen over 30 years old being eligible.
By lot, two out of three prisoners Sam, Jean, and Chris are chosen to be executed.
These wines are labeled by lot numbers rather than vintage years.
Jockeys get traded a lot, but the horses each ward gets by lot can't be traded.
Similar(1)
The technology-by-lot-within-sire interaction was a significant variance source for PredPtY.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com