"Two solitudes" alludes to the 1945 novel Two Solitudes, by Hugh MacLennan, about the conflicts between English- and French-speaking Canadians. Today, the phrase usually refers to the way English- and French-speaking Canadians tend to live very separately from each other, with little culture or social life in common.
Here's why "two solitudes" makes sense in the context where you found it. Federalism is a "two-tier" form of government in which provinces each have their own government and there is also a national, or "federal", government. One approach to federalism would be to have a strict separation of jurisdiction and authority between the provinces and the federal government ("two solitudes"), where neither can impinge on the other's decisions—the federal government, say, attending to foreign policy, national defense, monetary policy, and inter-province commerce, and each provincial government attending to commerce within its own province, education within its own province, roads and infrastructure within its own province, etc. It appears that LeBel played an important role in decisions that established overlapping authority for the provinces and the federal government.
"Two solitudes" is an interesting, even poetic choice of words for a situation of strictly delimited authority between the federal and provincial governments. Because of the sad connotation of the word "solitude", it casts the federal and provincial governments as lonely people each tending silently to their own walled gardens on some cold, cloudy day. It suggests that they'd cheer up if they took down the walls and talked and worked together on the gardens, even though they won't agree about everything.
Because of MacLennan's novel and the term's use for Canada's cultural divide, the analogy with strict division of legislative powers might come across more clearly and with less of the poetic connotation to (English-speaking) Canadians than to other English speakers.
I just googled and found that the phrase first occurs in these two sentences of the novel: "He wondered if Heather had ever felt as he did now. Two solitudes in the infinite waste of loneliness under the sun." [link]