If I want to read a book on what it was like during the times Lincoln was alive would I want to read the Cultural,social or intellectual context of Lincoln's life?
That's an enormous and complex subject. It varied somewhat by region, more by urban or rural, near the frontier or long-settled, etc. But, especially it would depend on class, education, and wealth. I think you'll need a pretty big book!
My suggestion is Lincoln - The Prairie Years and the War Years by Carl Sandburg. Originally published in six volumes, it's now been condensed into one. IIRC, it won the Pullitzer Prize.