The deaths were recorded on Tuesday and Wednesday, and follow a previous death recorded on July 13, bringing the total number at hospitals run by University Hospitals of Morecambe Bay NHS Trust (UHMBT) to 584.
In recent months, there had been just one death recorded in both April and May, and none in June.
The deaths are recorded when someone has died after testing positive for coronavirus within the last 28 days at UHMBT hospitals, with the numbers roughly split between the Royal Lancaster Infirmary and Furness General Hospital in Barrow.
The number of people in trust hospitals being treated for Covid-19 is also increasing; as of Tuesday July 13, there were 24 patients, three of which were on a ventilator.
Since the start of the pandemic, as of Saturday July 10, UHMBT has treated 2.092 people for the virus.
On July 13, visits to all Morecambe Bay hospitals were stopped for at least two weeks due to rising coronavirus levels in the community.In the Lancaster City Council region itself, the total number of deaths within 28 days of first positive test result for Covid-19 reported up to Tuesday July 20 is 285.
The total number of deaths where Covid-19 is mentioned as a cause on the death certificate, registered up to Friday July 9 is 330.
The total number of people with a positive Covid-19 virus test (either lab-reported or lateral flow device) reported up to Tuesday July 20 in the Lancaster region is 12,668.
Of those, 856 people in Lancaster reported positive Covid tests in the seven days up to July 20 (an increase of 176 or 25.9 per cent on the previous week) - and the city currently has an infection rate of 435 based on a rolling seven-day period up to July 12.
This is based on the number of coronavirus cases per 100,000 people, and compares with an England average of 378.