"Lincoln Day" isn't a familiar phrase to me. When I was a child, we celebrated "George Washington's Birthday" on February 12th and "Lincoln's Birthday" on February 22nd. (They've now been combined into a single "President's Day," third Monday in February).
Abraham Lincoln belonged to the Republican party and Republicans are proud of Lincoln.
I see that in 2015, in Wheeling, "The Ohio County Republican Executive Committee proudly presents a Lincoln Day Dinner on July 22, 2015."
So I would guess that the "Lincoln Day Dinner" is a local Republican party tradition in Wheeling.
McCarthy's speech in Wheeling is famous/infamous. I'm sure this is all in the book, but that's the speech in which he held up a piece of paper and said "I have here in my hand a list of 205 names that were made known to the Secretary of State as being members of the Communist Party and who nevertheless are still working and shaping policy in the State Department." He refused to show reporters the "list," giving various excuses, and in subsequent speeches the number he claimed were on the list kept changing--as well as his description of their degree of affiliation with the party (were they actually "members" or merely "loyalists," etc.) (In short, the "list" did not exist and he couldn't even remember what he had previously said about it).