The Augustana Synod consisted of Swedes and
the ALC consisted of Norwegians. So they waited
until 1962 to join their fellow Swedes in the LCA.
Why would that matter? They were in fellowship with The American Lutheran Conference from 1930-1960 with the Norwegians...
Time-out for clarification.
The synodical alliances of that time period are sometimes hard to understand. First of all, one must distinguish between the "old ALC" formed in 1930 (consisting of three/four different German background synods) and the "new ALC" of 1960 (made complete in 1963 when the Lutheran Free Church joined it), officially abbreviated "TALC" to distinguish it from the old, German ALC. The American Lutheran Church of 1960/63 (TALC) consisted of the Evangelical Lutheran Church, ELC, (Norwegian, and the largest group of the merger), the "old" ALC of 1930 (German in background), and the United Evangelical Lutheran Church, UELC, (Danish in background, of the "sad" variety from the Danish "inner mission" tradition as opposed to the other Danish group that joined with the LCA in 1962). Compared to the ELC and ALC, the UELC was quite small, comprising only about three percent of the membership of the new TALC. And as I said, in 1963, the Lutheran Free Church (also of Norwegian background) finally mustered enough votes to join TALC, but about 20 percent of its congregations declined to merge, and instead formed a new group call the Association of Free Lutheran Congregations, AFLC.
As to why the Augustana Evangelical Lutheran Church (Swedish) did not join TALC and instead joined the LCA, that is a complex matter, but I'll try to explain. In the years leading up to the mergers of the 1960s, there were three broad groupings of Lutherans in the United States. The one would be the Synodical Conference, which included the Missouri Synod, regarded as the most doctrinally rigid of the three. On the other end of the spectrum was the ULCA, regarded as the least doctrinally rigid. In the middle was a type of "protective alliance" of a few different synods called the American Lutheran Conference. These were groups that participated with the ULCA in the National Lutheran Council, but feared the influence of the ULCA in theological matters. The American Lutheran Conference folks were not quite as doctrinally rigid as the Synodical Conference folks, but they shared a greater kinship with the Synodical Conference than they did the ULCA. The American Lutheran Conference consisted, I think, of the following groups: ELC (Norwegian), ALC (German), UELC (Danish), Lutheran Free Church, Augustana Evangelical Lutheran Church. Maybe I'm missing one or two in there. But numerically, all three groups were about the same size. Note here that the Augustana Church identified itself with these more doctrinally rigid groups.
The American Lutheran Conference, which was based on the Minneapolis Theses of 1925, written by Hans Gerhard Stub, the first president of the ELC, became the foundation for the eventual merger that produced the TALC in 1960. Why, then, didn't the Augustana Swedes join them? Well, historically, the Augustana Synod had ties to the eastern Lutheran groups that went on to form the ULCA in 1918. They were originally a part of the General Council, but they declined to participate in the 1918 merger, pursuing an independent future. And so they were pulled in a couple of directions. Theologically, they tended to agree with their American Lutheran Conference sister synods. But they also felt that merger negotiations should be open to all Lutherans who wanted to participate. But the rest of the American Lutheran Conference wanted to exclude the ULCA from negotiations. And that is what caused them to merge into the LCA in 1962.