At least one of the lawsuits against Trump appear to be headed to a supreme court which includes his appointees. Has anything like this historically occurred, perhaps in a lower court? If so, Did those justices recuse themselves and/or what was the public and political fallout?
I'm sure someone can come up with a fuller list, but Clinton v Jones comes to mind immediately. Both Ginsburg and Breyer were Clinton appointees, and Breyer even wrote a concurring opinion (the case was decided unanimously). I don't recall there being any fallout from them specifically being involved.
Every judge has to be appointed by the President and confirmed by the Senate. As such, the mere act of having been appointed by a person does not appear to be grounds for recusal.
Additionally, judges (especially at the SCOTUS level) are given fairly broad discretion to recuse themselves. Anonin Scalia famously did not recuse himself from a case involving Vice President Dick Cheney solely because he and Cheney had been on a hunting trip together
"I do not believe my impartiality can reasonably be questioned," Scalia said in a 21-page memorandum, rejecting suggestions of an appearance of a conflict of interest.
"If it is reasonable to think that a Supreme Court Justice can be bought so cheap, the Nation is in deeper trouble than I had imagined," he wrote.
Recusal also tends to have negative connotations, which makes it unlikely
“Supreme Court justices rarely recuse,” University of Michigan Law School professor Richard Primus said. “For Kavanaugh to recuse would be for him to say, ‘Yes, I understand you don’t trust me ... and I validate that concern.’ He’s not going to say that.”
Federal law requires a justice to disqualify himself from deciding cases “in which his impartiality might reasonably be questioned.” In a 2011 report, conservative Chief Justice John Roberts said he had “complete confidence in the capability of my colleagues to determine when recusal is warranted.”
In United States v. Nixon however "Justice William Rehnquist recused himself as he had previously served in the Nixon administration as an Assistant Attorney General". Rehnquist was also Nixon-nominated to the Supreme Court, but he didn't include in his recusal the latter reason. The same Court also had Nixon-nominated justices Harry Blackmun and Lewis F. Powell Jr. on board, neither of whom recused, and even the Chief Justice of that court, Warren Burger, had been nominated by Nixon himself.
I think the fact that there is a Senate confirmation for Supreme Justices makes the nomination remote enough not to be a reason for recusal. I'm not sure anyone has argued it explicitly along these lines though.
One pretty long review paper on recusals argues that
A more demanding recusal standard is possible at the lower federal court levels precisely because recourse is available--other judges are available to be substituted. At the Supreme Court level, however, precluding Justices from hearing cases for purely remote precautionary reasons, and thereby silencing important voices in the decision-making process, is impolitic, unwise, and counterproductive.
If, indeed, "the judgments that the President and the Senate are supposed to reach in the nomination and confirmation processes are essentially political judgments-in both the highest and lowest senses of that term," then Supreme Court Justices have, in fact, been selected because they hold particular biases. Having appointed a particular individual based on that person's ideology (and political connections) renders recusal due to bias as to those ideological issues incongruent.
What are the consequences when a Supreme Court Justice disregards the statutory proscriptions? The Justice will not be subject to a disciplinary hearing; the only real remedy would appear to be impeachment.
Speaking of which there was at least one Supreme Justice, Abe Fortas, who resigned under threat of impeachment (during Nixon's presidency). Although Fortas was accused of some conflicts of interest, these didn't involve the president.