Lothian Buses is the largest municipal bus company in the United Kingdom. the City of Edinburgh Council (through Transport for Edinburgh) owns 91%, Midlothian Council 5%, East Lothian Council 3% and West Lothian Council 1%. So saying Lothian Council has no control is misleading.
Im by no ways an expert in councils, however this much is true. There is no such thing as "Lothian Council"...
Edinburgh Council
East Lothian Council
West Lothian Council
Midlothian Council
Are all entirely separate and are in no way connected, their all different authorities in different jurisdictions. Their separate councils, different budgets, different councillors and different aims.
(Similar to East Ayrshire Council, North Ayrshire Council and South Ayrshire Council)
That being said, Lothian Buses ownership is split between four authorities. This doesn't mean they have any say in what the company does, in anyway. Council owns the company, company operates the services, Council does Council things like not fixing roads.
By all means, they could request services etc but the company can say no. Its a commercial operation that just happens to be owned by the four councils.
An arms length company - pretty much a modern interpretation of municipal ownership.