How did Lincoln's economic policy set the GOP on their path towards corporate domination?
To be fair, I do approve of much of Lincoln's economic policy - the first income tax, the use of greenbacks, land grant colleges, etc. - so it's more that there are a couple areas of economic policy where I think Lincoln's administration had that effect, and the extent to which I think it's fair to hold Lincoln accountable for the long-term implications varies:
Procurement: to be fair, Lincoln inherited a Federal government that really didn't have a modernized procurement system. However, between that and the pretty thorough corruption of Secretary of War Simon Cameron and others within the Federal government, a lot of businessmen got rich selling substandard goods to the Union army and navy at a markup in exchange for kickbacks - so much so that the term "shoddy" became generalized and popularized as a result. (Previously, "shoddy" had specifically referred to reprocessed wool.)
Bonds: in order to finance the Union war effort, the Lincoln administration sold an enormous amount of bonds - and Treasury Secretary Salmon P. Chase basically turned the Union's bond drive over to Jay Cooke, a politically-connected Philadelphia banker. To give him credit, Cooke was very good at selling bonds both to ordinary bankers and the man on the street, but Cooke's personal commission meant that he (and the men he hired as his sub-agents) became staggeringly wealthy and thus a major donor to the Chase presidential campaign in 1868. Cooke ultimately was bankrupted when his Northern Pacific Railway went bust in the Panic of 1873.
Banking: while the National Banking Act of 1863 had many good elements - nationalizing the currency, and establishing Federal charters that allowed the Federal government to regulate banks on capital and reserve requirements - it also had the effect of further concentrating currency and credit in Northeastern banks (which could more easily meet those requirements due to being better-capitalied to begin with), which was a bit of a problem when you realize that the U.S didn't have a central bank to ensure that all regions of the country had decent access to currency and credit.
Railroads: the Pacific Railroad Acts of 1862 and 1864 provided for the Federal subsidization of transcontinental railroads through the granting of Federal land. While this got the railroads built, it didn't come without a healthy side-order of corruption: understanding that they stood to make a fortune if the railroad acts went through, railroad companies gave out a lot of free stock to U.S Congressmen, who in turn made sure the Acts passed and the Federal government was generous with land grants, loans, etc. This wouldn't blow up until the Credit Mobilier scandal of 1872, but the roots go back in the 1860s.
As you might expect, a lot of the bankers and railroad executives who had gotten rich off the Civil War became major donors and activists and party leaders and elected officials of the Republican Party. This had a significant impact on the party's political and policy direction: by 1868, the Republican Party's national platform mixed calls for civil rights and equal suffrage with demands that Civil War debt be redeemed in gold rather than paper money (which contributed to post-war deflation and represented a repudiation of the Greenback Acts), and that progressive taxation be done away with.
