Both main parties, as has variously been noted, are broad coalitions. That is especially true of the Labour Party, which has a history of factionalism. If either party enters into a coalition with the Liberal Democrats, it may cause tensions within the party. There is a section of the Labour Party that would be opposed on ideological grounds. There are some in the Labour Party who would find it objectionable for local tribal reasons. In some areas, the rivalry between Labour and the Liberal Democrats is intense. There are parallels on the Conservative side.
However, the Liberal Democrat party is also a broad coalition. It was formed from a merger of the Liberal Party and the Social Democratic Party. Some former Labour MPs who joined the SDP now sit on the Liberal Democrat benches in the Lords. The Liberal Party itself was a broad church, prone to splits and indeed having prominent leaders who notably split the party on the basis of policy or personality. The party never recovered fully from the split between Lloyd George and Asquith. The Liberal Democrats have some who are ideologically inclined to the Labour Party but others who lean towards a more market philosophy. The party has carved out different messages in different parts of the country depending on the nature of its opponents. How would Liberal Democrats holding seats in the West Country by virtue of winning votes from potential Conservative voters justify an alliance with the Labour Party?
A coalition with either main party carries enormous risks for the party. It will be interesting to see if the Liberal Democrats emulate their Liberal forebears.