The bus company entered administration earlier today with 1,200 jobs lost in Northern Ireland due to its collapse.
Administrators confirmed only 50 jobs would be kept at the firm, which also supplied London with new Routemaster buses while Boris Johnson was Mayor of London.
However, the company had suffered cash flow problems and in July said it was seeking a new buyer.
It is not yet clear how the administration could affect Lothian, but in 2016 the two companies announced a four-year partnership with Wrightbus supplying 316 buses to Lothian.
The deal, which began in 2017, was due to end in 2021, with all of the buses on the order delivered to the bus operator, but Lothian have yet to confirm whether there is a contract in place for the supply of spare parts or if there is any further impact due to Wrightbus' administration.
The vast majority of spare mechanical parts are supplied by Volvo who build the chassis of Lothian's fleet.
Wrightbus' administration will not affect future orders of the triple axle 'super buses' which are supplied by bus manufacturer Alexander Dennis.
Richard Hall, Lothian managing director, said there was no "significant risks" to the business due to Wrightbus' collapse.
He said: “Lothian has worked closely with Wrightbus for an extended period as one of the key UK Bus Manufacturers. Our first thoughts are with the Wright family and the many employees and their families affected directly by this news.
“We are proud to operate a significant number of Wrightbus vehicles as part of our fleet, alongside those from our other key body partner Alexander Dennis. Both are based on the renowned Volvo chassis product, which are maintained by our skilled in-house engineering teams.
“Buses are of modular construction utilising a wide number of third party manufacturers components, many of which we already enjoy long established relationships with. As such we currently see no significant risks to our business, though we and the rest of the bus and coach industry would still hope that elements of the Wrightbus business could be saved by the receivers Deloitte.”