A total of 300,000 passengers flew between Edinburgh, Aberdeen and Lufthansa's main Frankfurt hub, and with Brussels Airlines between Edinburgh and the Belgian capital.
The increase from 2.1 per cent growth in 2015 came despite Brussels airport being closed for two months following a terrorist attack last March.
UK senior director Andreas Koster said Lufthansa had also cut seat capacity by 16 per cent on the Aberdeen route by using smaller aircraft because of the downturn in the oil industry.
He said the airline was upgrading its airport lounges and introducing new aircraft to improve quality and help take on increased competition, such as from Ryanair, which is to fly to Frankfurt's main airport for the first time after previously using Hahn, some 90 minutes away.
Lufthansa has also pledged to retain free food and drink, unlike some rivals like British Airways which have axed it on short-haul flights.
Mr Koster welcomed the minority Scottish Government's planned halving of the £13 air passenger duty (APD) on short-haul flights - if it is passed at Holyrood.
However, he said it was too early to predict its impact amid other potential factors, such as Brexit and airline competition.
He told The Scotsman: "If you reduce it, you reduce fares and trigger demand, without doubt.
"There may be a big potential for APD, but it may be offset by other effects."
Mr Koster said the tax reduction could potentially lead to fellow group airlines Austrian and Swiss launching routes in Scotland.
He said: "Other brands could be an option, depending on the development of demand.
"I'm not saying a new brand will come to Scotland next year, but we have the flexibility if there is demand for that."