It seems the ice is cracking on Babbitt's killer,

and it's getting interesting.

Now a new name has surfaced in the Babbitt imbroglio — Lt. Michael L. Byrd — and while USCP Communications Director Eva Malecki won’t confirm he is the shooter, in this case she isn’t denying it.
...
In addition, Byrd’s resume lines up with what is known about the experience and position of the officer involved in the shooting — a veteran USCP officer who holds the rank of lieutenant and is the commander of the House Chamber Section of the Capitol Police.

Following the shooting, Byrd’s Internet footprint was scrubbed, including his social media and personal photos.

This is interesting:
In February 2019, Lt. Byrd was investigated for leaving his department-issued Glock-22 firearm unattended in a restroom on the House side of the Capitol, even though the potent weapon, which fires .40-caliber rounds, has no manual safety to prevent unintended firing. Fortunately, the abandoned gun was discovered by another officer during a routine security sweep. A Glock-22 was used in the Babbitt shooting.

Byrd addressed the blunder at a roll call the following morning, reportedly telling fellow officers that he would “be treated differently” because of his rank as a lieutenant.
The lawsuits are being filed, and they're pushing for more information.  I'd say this is going to get messy.

As to whether justice will be done?  Considering the agency, and our current 'Justice' Department, I doubt it, but I'd be happy to be surprised.