I hate to be that guy, but first, it's "secession" not "succession".

Second, I encourage you to not take anything in that book too seriously. It's historical fiction, not history, and as such, the writer takes some storytelling liberties. While I am less familiar with the book than the movie adaptation of it, the movie is widely criticized for promoting Lost Cause propaganda. (Example 1, Example 2, Example 3, Example 4.)

With that out of the way...

Threats of disunion and secession were widely known by the time South Carolina actually seceded. I would be surprised to find anything in Lee's writing to suggest he was unfamiliar with secession before November 1860, though I could imagine he may have been skeptical of it ever actually happening. That's because threats of secession had been common for thirty years before the Civil War. It came up any time there was a political flashpoint. Even before the 1830s, there were common threats of disunion. Most of these threats were slavery-related, and universally so after 1830.

The most significant secession threat before the Civil War was the Nullification Crisis in 1832-33. South Carolina passed an Ordinance of Nullification, protesting against a federal tariff they didn't approve of ("the Tariff of Abominations"). The law ended with a threat of secession:

"... the people of this State will henceforth hold themselves absolved from all further obligation to maintain or preserve their political connection with the people of the other States; and will forthwith proceed to organize a separate government, and do all other acts and things which sovereign and independent States may of right do."

President Andrew Jackson sent federal troops to the port of Charleston and there was a standoff between the federal government and the State of South Carolina and their state militia. While it was resolved peacefully, it produced commentary far and wide about the right of secession. There was a famous debate on the Senate floor on the subject known as the Hayne-Webster Debate. The speech known as "Webster's Second Reply to Hayne" repudiating the right of secession, and calling for a loyal union, was called by at least one 19th Century commentator the most famous American speech before the Civil War, after George Washington's Farewell Address (another speech that advocates for national unity).

The Nullification Crisis also created a politican faction based in South Carolina known as the "Nullifiers". They were essentially active from that point until the Civil War. It's at least arguable that the Southern Democrat "Fire-Eaters" were an expansion of the South Carolina "Nullifiers" and their political ideas, just spread throughout the South.

The next big flashpoint of disunion and secession occurred during 1850, which led to the Compromise of 1850. There was much discussion then of secession and war. In the book Southern Pamphlets on Secession edited by Jon L. Wakelyn, an 1850 pamphlet is reproduced, entitled "The Position and Course of the South", written by William Henry Trescot. The pamphlet advocates for secession of the slave states, and gives its reasoning, arguing:

"But one safe path is open to her [the South's] honour, and that is, Secession and the formation of an Independent Confederacy."

One of the more famous speeches given in relation to the crisis of 1850 was the March 4, 1850, speech by John C. Calhoun, former Vice-President and Senator from South Carolina who had played a role in the Nullification Crisis almost two decades earlier. The speech was given less than a month before he died:

"Unless something decisive is done, I again ask, What is to stop this agitation before the great and final object at which it aims—the abolition of slavery in the States—is consummated? Is it, then, not certain that if something is not done to arrest it, the South will be forced to choose between abolition and secession? Indeed, as events are now moving, it will not require the South to secede in order to dissolve the Union. Agitation will of itself effect it, of which its past history furnishes abundant proof..."

Three days later, the ardent unionist Daniel Webster, who had also been a figure in the Nullification Crisis, gave a response to the Nullifiers and those threatening disunion:

"A voluntary separation...Why, what would be the result? Where is the line to be drawn? What States are to secede? What is to remain American? What am I to be?—an American no longer? Where is the flag of the Republic to remain?"

A great source, and quite readable, is the book Disunion: The Coming of the American Civil War 1789-1859, by Elizabeth R. Varon. The author recounts the entirety of disunion/secession efforts in U.S. history before the Civil War. Among other examples in relation to the crisis of 1850, Varon recounts a letter sent by a constituent to Sen. Salmon Chase of Ohio (a Free Soil Democrat who would later become a Republican, and serve in the Lincoln Administration as well as Chief Justice of the Supreme Court). Chase offered a response, as Varon recounts:

"The constituent, L. S. Abbott, had sent Chase a petition urging a 'peaceful separation of the Union.' Chase gently rejected the petition, explaining that it was not 'beneficial to the great cause.' Chase understood that Abbott’s main objective was 'to let the South see that you cannot be intimidated by threats of disunion.' But the best way to do that, Chase advised, was to critique the 'aggressions of the Slave Power' and petition for 'the removal of slavery from the whole sphere of exclusive national jurisdiction, without regard to Southern menaces of dissolution.' Disunionism, Chase elaborated, was defeatist..."

Secession, disunion, and war was such a big topic in 1850 that it was the subject of political cartoons. Varon reprints one entitled "The Hurly Burly Pot" which has abolitionist William Lloyd Garrison saying: "Till disunion come!" Garrison was the rare Northerner who advocated for secession, on the basis that the U.S. Constitution's protections of slavery made the document a "covenant with death" and an "agreement with hell". (Warning: the above-linked cartoon includes some racial slurs.)

The debates in Congress in 1850 got so heated that at one point Sen. Henry S. Foote of Mississippi drew a pistol on Thomas Hart Benton of Missouri.

Throughout the 1850s, the threats of secession continued, including in 1854 with the Kansas-Nebraska Act, in 1856 with the Presidential election and the prospect of the anti-slavery Republican candidate John C. Frémont getting elected, and then from 1859 after John Brown's Raid and throughout the 1860 campaign. Famously, blood was so bad that violence in Congress continued. On May 22, 1856, after giving an anti-slavery speech against a fellow senator, Sen. Charles Sumner of Massachusetts was almost beaten to death on the Senate floor by Rep. Preston Brooks of South Carolina (a second-cousin of the senator that Sumner had spoken against).

In the lead-up to Abraham Lincoln's election in 1860, secession, disunion, and war were common topics. There was discussion of it in Congress, as well as in the press. The companion books Southern Editorials on Secession edited by Dwight Lowell Dumond, and Northern Editorials on Secession edited by Howard Cecil Perkins give almost two hundred examples of newspaper editorials on secession between the beginning of 1860 and Election Day—and 200+ more after, until all eleven Confederate states had seceded. Some editorials promote secession, some denounce it, but it was clearly a hot topic throughout the country up to and after Lincoln's election. I'll just provide a couple of brief quotes:

On October 11, 1860, the Charleston Mercury ran an editorial listing all the supposed terrors that await the South if Lincoln is elected. They conclude by saying secession is the safer option than staying in the union if Lincoln gets elected:

"...[W]e conclude this brief statement of the terrors of submission, by declaring, that in our opinion, they are ten-fold greater even than the supposed terrors of disunion."

On October 30, 1860, the Louisville Daily Journal endorsed Constitutional Unionist John Bell for President, rejecting both Lincoln and Breckinridge, calling the latter the "Seceding candidate":

"...[M]en of the Union, defeat the Republican candidate and the Seceding candidate equally, rout Lincoln as well as Breckinridge and Breckinridge as well as Lincoln, and Disunion in both its aspects and in every shape will be vanquished and extinguished. Do this, and you will put an end to Disunion forever. Positive Disunion will be stifled and there will be no negative Disunion to restore it. Do this, and the frowning thunder-cloud will part not to discharge its red bolts of death but to melt into the sunlight of enduring peace. This and this only will constitute the triumph of the Union."

In summary, if Gods and Generals truly makes it seem as though the suggestion of secession comes as a surprise to Robert E. Lee, then it's not historically accurate. It was one of the major issues of the 1860 campaign, and a regular political issue throughout Lee's adult life. If the suggestion is that Lee is surprised it's actually finally happened, after so many failed threats, that's more believable.

TL;DR: Robert E. Lee, and the American public, would have been very familiar with the threat of secession before Lincoln's election.