Finance director Graham Moorhouse is understood to have walked out of the taxpayer-owned firm last Monday.
His predecessor Norman Strachan left the £150,000-a-year post in acrimony last January after a well-documented and bitter row among bosses.
Tory Councillor Jason Rust said: “It’s very concerning for our publicly owned bus company that it has lost a second finance director in such a short space of time.
“Given the previous travails at Lothian buses at director level and the amount of public investment in its fleet, it is vital that there is experienced financial leadership and strategic direction.”
The Evening News reported last month how much vaunted hybrid buses were withdrawn from a busy city route because the Capital’s hills were proving too much for them.
A fleet of 15 electric-diesel double-deckers was introduced on the No 10 route from Western Harbour to Bonaly and Torphin seven years ago. But the buses had to be replaced by diesel alternatives much to the dismay of some passengers.
Sources within the company said the hybrid buses were having “battery issues” with the “hilly” route and most are now being retrofitted with diesel engines.
The first hybrid double-decker fleet to operate in Scotland, the buses were launched at Holyrood in 2011 by the then Transport Minister Keith Brown to much fanfare. They cost £5 million, of which £1m was funded by the Scottish Government’s Green Bus Fund and were said to cut carbon emissions by nearly a third.
Mr Moorhouse joined Lothian buses as finance director earlier this year, having previously held a similar role at the plush Dalmahoy Hotel and Country Club.
Former finance director Norman Strachan hit the headlines last September over fat cat pay after getting a £150,000 golden handshake when leaving the firm. Mr Strachan was one of the trio dubbed the “Annandale Three” – after the city’s main bus depot.
The senior managers fell out with former chief executive Ian Craig, claiming he failed to consult them on major decisions. An investigation upheld five grievances, including an allegation Mr Craig spent £269,000 on the brand launch for umbrella body Transport for Edinburgh without their knowledge and that staff “disappeared from employment with no discussion with the board”.
After a failed mediation process, chair Ann Faulds recommended Mr Craig’s dismissal, but resigned when the council refused to back her.
Mr Craig later stepped down and the other three, including Mr Strachan, also agreed to go.
A Lothian buses spokesperson said: “We don’t comment on speculation regarding staff”.