Lancaster Magistrates heard that the e-cigarette kiosk at EN Newsagents in Orchard Street sold e-liquid to a 15-year-old volunteer on August 9, 2021.
The same staff member went on to sell disposable e-cigarettes to a 16-year-old volunteer on November 19, 2021.
Gulam Patel, who owns the business, was fined £166 and ordered to pay £275 in costs.
The shop assistant, Maqbul Hussain, who sold the products on both occasions, was fined £130 and ordered to pay £275 in costs.
County Councillor Peter Buckley, Cabinet Member for Community and Cultural Services, said: “This case sends out a clear signal that we won't tolerate anyone selling vaping products to children under the age of 18.
“In many instances, we work with businesses to ensure they comply with the law and act responsibly.
“However, where necessary, we will not hesitate to prosecute, especially where previous advice is ignored.”
Trading Standards carried out the operations in response to an increase in the number of complaints relating to underage sales of vaping products.
It is a criminal offence to sell nicotine inhaling products to anyone under 18.
Nicotine inhaling products include e-cigarettes, cartridges and e-liquids.
"Our Trading Standards team will be continuing with test purchasing to ensure businesses are fulfilling their legal obligations,” Mr Buckley added.
“They are also on hand to provide advice and guidance to businesses that need support.”
County Councillor Sue Whittam, Lead Member for Health, said test purchasing operations were “crucial” in helping the council clampdown on underage sales.
"For young people who don't already smoke, vaping can be a gateway to smoking cigarettes, potentially beginning a habit that can be extremely damaging to their health and wellbeing,” she added.
“Some of these devices can also deliver very high levels of nicotine, which is also a concern.
"The low prices, fruity flavours and brightly coloured packaging of many of these products mean they can be very appealing to under-18s, so taking enforcement action like this is crucial so we can limit opportunities for young people to buy them."