Cllr Jim Buchanan, a Conservative councillor, is the new leader of Cumbria County Council. It means that every county council in the country has a Conservative leader. Independent and Labour councillors will be joining the coalition. The Lib Dems will become the official opposition.
Even if the Lib Dems had accepted a Cabinet post, Cllr Buchanan would have had a casting vote to avoid deadlock. As it is the Conservatives will have a majority of cabinet posts.
There could have been a minority Conservative administration formed and a Conservative/Labour coalition is something of an oddity. But I get the impression that there isn't a great ideological clash in Cumbria.