President Obama did not order that the White House be lit in blue to commemorate police officers slain in the line of duty.
He did not neglect to honor their sacrifice in other ways, such as flying flags at half-staff; there is no evidence that he specifically "refused" to light up the building in blue.
On the evening of 15 May 2017, the White House was illuminated in blue light to commemorate Peace Officers Memorial Day, a national observance for fallen police officers instituted by President John F. Kennedy in 1962.
President Trump noted the occasion in a tweet linking to his 2017 Police Officers Memorial Day proclamation:
— Donald J. Trump (@realDonaldTrump) May 16, 2017
"Police officers are the thin blue line whose sacrifices protect and serve us every day, and we pledge to support them as they risk their lives to safeguard ours," the proclamation said:
In humble appreciation of our hard-working law enforcement officers, Melania and I will light the White House in blue on May 15. I call upon all Americans to observe Peace Officers Memorial Day and Police Week with appropriate ceremonies and activities. I also call on the Governors of the States and Territories and officials of other areas subject to the jurisdiction of the United States, to direct that the flag be flown at half-staff on Peace Officers Memorial Day. I further encourage all Americans to display the flag at half-staff from their homes and businesses on that day.
Conservative-leaning media outlets seemed to unanimously point out in their reporting on the event that President Barack Obama had, in their words, "refused" to memorialize fallen officers with blue lighting after five Dallas policemen were killed by a sniper in July 2016.
For example, the Washington Examiner reported:
Former President Barack Obama lit the White House in rainbow colors after the Supreme Court ruling that allowed same-sex couples nationwide to marry in June 2015.
Following the attack on police officers in Dallas last July, the Federal Law Enforcement Officers Association Foundation asked Obama to illuminate the White House in blue in honor of the five fallen officers. Obama ordered flags to be flown half-mast, but did not light up the 1600 Pennsylvania Avenue NW building.
Contemporaneous press reports confirm that despite the Federal Law Enforcement Officers Association's request, the Obama administration chose other means to memorialize the Dallas victims. White House Press Secretary Josh Earnest spoke about the decision during a 13 July press conference:
REPORTER: The Federal Law Enforcement Officers Association announced on Friday that they may request to the White House that it be illuminated in blue in honor of the fallen officers in Dallas. Knowing that the White House has previously been illuminated, both in 2013 in pink for breast cancer awareness and again in 2015 in the wake of the same-sex marriage ruling by the Supreme Court, has there been any consideration or any thought given to lighting the White House in blue in honor of law enforcement?
EARNEST: I don't have much to say about the potential consideration. I can tell you that's not something that we plan to do at this point. The President certainly has, in a variety of ways, acknowledged the tragedy and honored the life of the five Dallas police officers who were killed last week. The President, while he was overseas, ordered flags across the country lowered to half-staff as the nation mourns the loss of those police officers. And, of course, the President traveled to Dallas just yesterday to speak at the memorial service that was organized to honor their service and honor their sacrifice.
And after that service concluded, the President spent more than an hour with the families of those who were lost and spent time visiting with some of those who were injured, including police officers who were injured in that shooting. So there are a variety of ways that the President and this administration have chosen to conspicuously demonstrate our deep gratitude and our solemn condolences in the aftermath of the shooting that claimed the lives of five police officers in Dallas last week.
Notably absent from the Obama administration's explanation of the matter was why the idea of blue lighting was nixed, though it clearly was. As Josh Earnest stressed, Obama did commemorate the Dallas tragedy in a variety of other ways, including flying flags at half-staff and visiting with injured officers and the families of those who were slain.
As reported elsewhere, the White House was illuminated on other occasions during Obama's occupancy, including bright pink in honor of Breast Cancer Awareness Month (an annual tradition started by George W. Bush) and in rainbow colors to celebrate the Supreme Court ruling in favor of gay marriage in 2015:
— White House Archived (@ObamaWhiteHouse) June 27, 2015
President Trump has ordered the use of blue lighting on the White House on one previous occasion, World Autism Awareness Day on 2 April 2017.
A distinction that ought to be made is between the sort of event Obama was asked to observe with blue lighting (the commemoration of five police officers murdered in Dallas in 2016) and the one President Trump observed (Peace Officers Memorial Day, held annually on 15 May). Regarding the latter, President Trump and every previous president since JFK, Obama also observed Peace Officers Memorial Day, with flags flown at half-staff and proclamations honoring the service and sacrifice of law enforcement officers.
Blue lighting, however, does not seem to have been on his agenda.