The snarky answer would be "much better than it was at 10:59 last Saturday morning." The truthful answer is that those who say don't know and those who know don't say.
You have to remember UT is in a really unique place in that Austin is the largest city in the U.S. without a pro sports franchise to share its primary media market with and the demographics of Austin are a dream for sports programming (young, college educated and somewhat sophisticated). Austin /Round Rock is also larger than San Fran (1.75 mil today) and growing quickly (projected to be 2.75 mil by 2030). The LHN was originally intended to be a 2 school vehicle to monetize T3 rights (such as what the Pac12 has developed) but ESPN took quick notice of the unique marketplace UT Austin has and they decided to take a chance on funding LHN.
In asking how LHN is doing, you have to ask "Compared to what expectations?" LHN costs Disney/ESPN about $50mil/yr all in (fees to UT and operating expenses. ESPN annual revenues are around $1.3B/yr.
Why ESPN Is Worth $40 Billion As The World's Most Valuable Media Property - Forbes
So, without selling a dime in ads or receiving a dime in carriage fees, the cost of LHN to ESPN is negligible. Worst case, its a long term option. My guess is that it is probably close to breaking even on an operating basis. Consider the value of the opportunity to learn lessons that they can leveraged in setting up SECN, the opportunity to train young technical and on air staff (Sam Ponder seems to have benefited from her time at LHN ) and the ability to work out operational issues they will need to have down for SECN, the cost of LHN is small. My sneaking suspicion is that ESPN Deportes will find more than a few key personnel shifted from Bristol to Austin over time. One thing that has been hugely interesting is how wealthy Mexican businessmen have been buying homes in gated communities between San Antonio and Austin over the past 10 years and having their families live safely in these houses while the men do business in Mexico.
Austin is going to be an incredible city to have an individual sports network in moving forward. Over time, they will work out content (If the University gets a world class sports medicine and orthopedics facility in the new on campus hospital, think of the athletes from both the U.S. and Latin American who will be in Austin to train and rehab. Talk about some interesting content for ESPN...). For now, whatever drain there is isn't material. I think they see value in being in Austin, they are probably at least close to breaking even on an operating basis and LHN fees they pay to UT are a sunk cost. Their presence in Austin is worth the cost of how they got there and I think they are smart enough to make money for ESPN because of the deal, even if it doesn't flow through the LHN balance sheet.
All in all, no one at ESPN is losing sleep over their presence in Austin or the cost of maintaining their facilities there. In fact, i think some younger guns are licking their chops to show what they can do with the LHN asset.