One of the three commercial units on the site is the Former Frankie and Benny's restaurant, which closed in July 2020, with the loss of 20 jobs.The other two units are the former Blockbuster Video shop, which is now a gym, and the Domino's Pizza shop next door.
The council purchased the land from London based real estate company Breathfull 1 Ltd in March.
A Lancaster City Council spokesperson said that the land will continue in its current use under existing leases held by the occupiers of the three commercial units.
They added: "All the commercial units currently have leases in place.
"The financial difficulties of the leaseholders of the largest unit, The Restaurant Group trading under Frankie and Benny’s, have been well documented.
"The company has entered into a Company Voluntary Agreement and the council is awaiting notice of their intentions with regard to the lease."
After the council bought the land, motorists were stung by Penalty Charge Notices (PCNs) for the car park, which were an arrangement between the previous owner and their car park management operator, a company called Civil Enforcement.
The council said that when it became aware that the company had been issuing PCNs without its authority, it told them to stop.
A spokesperson said: "The city council purchased the land in March and was unaware until very recently of the status of the car parking arrangements between the previous owner and their car park management operator.
"As soon as it came to our attention that the company had been issuing Parking Charge Notices (PCNs) without our express authority we took immediate steps for them to cease.
"We also advised them to remove their equipment and to cancel any PCNs issued since 27/3/20.”
The purchase of the land in Hilmore Way follows Lancaster City Council's purchase of the Wilko building in Lancaster city centre for £3.4m, earlier in March.
The council said at the time that the purchase of 17-21 Penny Street was the first in a number of investments the it is looking to make to help fund services.
The council's General Fund Capital Programme, agreed by councillors in February, earmarks £16m a year for property investment acquisitions over the next four years, totalling a potential £64m in borrowing.