What is the smallest launch vehicle, by dry mass, to have delivered a payload to orbit?
I am guessing that this might be either a re-purposed sounding rocket or something from the high-end of the model rocketry space.
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The Lambda 4S from Mark Adlers' answer has later been surpassed by another Japanese rocket, the SS-520, which successfully delivered a 4kg payload to LEO in 2018.
The total mass of the vehicle is 2,600kg, which with propellant subtracted is 610kg of dry mass.
As you correctly guessed, it's indeed a repurposed sounding rocket.
For dry mass, it appears to be Vanguard with a launch mass of 10,050 kg, and a dry mass of 1536 kg.