I’m going to attempt to remove the legal linguistics and explain what appears to be a highly predictable process most are ignoring.
BASELINE – After the 2018 mid-terms, and in preparation for the “impeachment” strategy, House Intelligence Committee Chairman Adam Schiff and House Judiciary Committee Chairman Jerry Nadler hired Lawfare group members to become House committee staff…. Chairman Schiff hired former SDNY U.S. Attorney Daniel Goldman (link), and Chairman Nadler hired  Obama Administration lawyer Norm Eisen and criminal defense attorney Barry Berke (link).  House Speaker Nancy Pelosi then hired Douglas Letter as House General Counsel – all are within the Lawfare network.
♦On October 25th DC Judge Beryl Howell granted the House Judiciary Committee (HJC) request for legal authority to receive 6e grand jury material underlying the Mueller report.
Additionally, within the Howell decision she officially recognized the HJC effort was predicated on a constitutional impeachment process.
In essence Howell’s opinion granted the HJC with “judicial enforcement authority.”
♦The DOJ moved to appeal the decision and requested a “stay” pending appeal.  Judge Howell rejected the “stay” motion.
The DOJ appealed to the DC Court of Appeals.  A panel of three judges issued an “administrative stay”, blocking enforcement of the Howell ruling while the appeal was reviewed.
The temporary administrative stay was granted to freeze the status quo while the court considers whether to grant a longer stay that would remain in effect until the DOJ appeal is argued or decided (deadline tomorrow).  The outcome is pending.  Judge Merrick Garland is the Chief Judge of the DC Appeals court.

After the full House voted to authorize the ongoing “impeachment inquiry” today, Nadler’s team immediately opened a second legal front.
♦Using the baseline predicate of Howell’s recognition of HJC impeachment authority; and now using the full House vote as further affirmation therein; the HJC is now moving to another Judge, Ketanji Brown Jackson, an Obama appointee to the federal district court in D.C., requesting judicial enforcement authority to compel testimony from former White House legal counsel Don McGahn:

WASHINGTON DC – Lawyers for the House Judiciary Committee urged a federal judge on Thursday to force former White House counsel Don McGahn to testify before Congress about President Trump’s possible obstruction of justice, arguing that his refusal to comply is harming House Democrats’ impeachment inquiry.
Democrats’ counsel said that even though McGahn’s role in the obstruction investigation carried out by former special counsel Robert Mueller was described at length in Mueller’s report, lawmakers still need to independently evaluate his testimony. (more)

The HJC objective is simple: gain judicial enforcement authority for their subpoenas so their targets cannot legally refuse to give testimony.
The premise for both fronts [(1) document subpoena 6e material, and (2) testimony from McGahn] is predicated on penetrating a constitutional firewall that exists within the separation of powers.
Under existing SCOTUS precedent, the White House can be compelled to deliver Executive Branch documents and testimony so long as an official legislative branch impeachment process is underway.
Judge Beryl Howell was the first person in the judicial branch to recognize and accept the HJC position that such an official impeachment process was ongoing.  Judge Brown Jackson will likely be the second. The House vote today is fuel for that twisted-legal approach.
Some have asked for my opinion on where this is going…. My opinion is not outlining success or failure, merely the likely approach they are taking with this scheme:
It would appear that Nadler and his Lawfare group are collecting evidence for their Impeachment Managers.  The decision to impeach was reached long ago; these moves by the HJC are moves to gather evidence for the Senate trial.
The Pelosi-Schiff optics of open House impeachment hearings is a pantomime, intended to give the illusion of customary and traditional impeachment proceedings taking place.  The impeachment report Schiff’s Lawfare group will deliver to the HJC Lawfare group is meant only to bolster the pre-existing conclusions from Barry Berke and Norm Eisen.
In essence, the usurpers began with the end in mind, and they are now back-filling the pre-scripted articles of impeachment with supportive evidence.   The HJC subpoenas are intended to do that back-filling along with the Schiff committee product.
Unfortunately, I do not foresee the DOJ succeeding in their appeals.  The DOJ has put their weakest lawyers (half-hearted attempts) into the fight.  As an outcome it looks like the Judiciary is aligned in favor of the constitutional predicate claimed by the HJC.

The judiciary (so far) doesn’t seem to be on the Trump administration’s side over the subpoena battles.

Today it’s Judge Ketanji Brown Jackson talking to a Justice Department attorney who is defending the White House.

— Shimon Prokupecz (@ShimonPro) October 31, 2019

Ultimately it will take a much stronger republican house effort to stop Pelosi, Schiff, Nadler and their host of Lawfare contracted agents.  Simultaneously it would take a much stronger team in the DOJ fighting to retain the executive branch position.  Neither is currently present.
Show me an action by U.S. AG Bill Barr to change the impression the DOJ is intentionally tanking the external fight and I will change my opinion.  However, so far the push-back from the DOJ has been very weak considering the stakes.  [Too weak to be accidental]
Thus my opinion: despite the strength of their constitutional position, the DOJ will fail to protect the office of the presidency.  It’s a gut-sense impression; but we should be able to get a better feel of DOJ motive from their approach toward the appeals court.
♦ That brings up the Senate trial.   From a review of their signaling and positioning, it appears to me the objective of the Lawfare group, via the impeachment managers, will center around modifications to Senate Impeachment Rules and the use of a Senatorial Trial Panel.
The senate rules on impeachment processes can be changed and modified [Example here from 1986].  Additionally there is nothing in the constitution that requires an established number of senators to sit or convict during the trial [Constitution, Article 1, Sec 3]:
This is my interpretation of what the Lawfare group will attempt.

“Concurrence of two-thirds of the members present“

The Democrats will argue their 2020 candidates cannot spend all this time on a Senate trial…. the media will be sympathetic….. Because the constitution is ambiguous to the construct…. and intentionally differential to the size of the Senate…. the democrat approach will be to empanel a bipartisan jury of an unknown number of Senators to sit for the trial “under oath and affirmation.”
There is nothing in the constitution that would stop the Senate from assembling a jury of 10 republican senators and 10 democrat senators. It would then require “two-thirds” or thirteen for a conviction.  Or the jury could be 40 or (fill_in_blank).
This type of a senate construct is what the left has been hinting about in their discussions.  This is what Lawfare has been discussing since they successfully gained the Nixon Impeachment Roadmap during their lawsuit a few months ago.