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All I can find about Lucius or Narcissa Malfoy, or their life after the Second Wizarding War, is that they were not sent to Azkaban and that they had a grandchild.
Is there any information about what happened to them and what they did after the Second Wizarding War? Were they ostracized by friends because they left the Death Eaters publicly? Were people scared to trust them?
Has J. K. Rowling given any information about what their life was like after the war?
Aside from the 2 facts you mentioned, Accio Quote lists absolutely nothing about Malfoys post-Voldemort-death. I searched for "Malfoy", "Malfoys", "Narcissa", "Lucius". Zero related references.
As far as them not going to Azkaban, that's true:
Georgina: Did lucius malfoy, and all the other escaped death eaters, go back to azkaban
J.K. Rowling: No, the Malfoys weaseled their way out of trouble (again) due to the fact that they colluded (albeit out of self-interest) with Harry at the end of the battle.
Source: J.K. Rowling and the Live Chat, Bloomsbury.com, July 30, 2007 (2.00-3.00pm BST).
An interesting side note is that Narcissa was not a Death Eater (Link).
This mostly just repeats information from @DVK’s answer, but makes it more explicit. In a Pottermore update, we learn that Lucius escaped capture by turning in other Death Eaters (not unlike Karkaroff in the first war):
Abraxas’s son, Lucius, achieved notoriety as one of Lord Voldemort's Death Eaters, though he successfully evaded prison after both Lord Voldemort's attempted coups. On the first occasion, he claimed to have been acting under the Imperius Curse (though many claimed he called in favours from high-placed Ministry officials); on the second occasion, he provided evidence against fellow Death Eaters and helped ensure the capture of many of Lord Voldemort's followers who had fled into hiding. His son, Draco, was saved by Harry Potter during the Battle of Hogwarts, and currently resides at the family estate in Wiltshire.
— The Malfoy Family, Pottermore (Transcript)
Narcissa lied to Voldemort and ensured that Harry’s survived to finish Voldemort, which would probably be sufficient to keep her out of Azkaban.
Draco was a Death Eater, but may have evaded capture on account of being too young. Alternatively, I think Harry might have recognised that Draco was acting partially under coercion, not completely free will, and might have offered him a second chance. Quoting from my answer to What happened to the Death Eaters?:
JK Rowling said in a 2007 interview with NBC that Harry and Ron “utterly revolutionised” the Aurors, and presumably Ministry justice systems. In Draco’s case, I think Harry saw the capacity for remorse, and might have been willing to offer Draco a second chance.
