There are lawsuits aplenty that have already been filed, but I'd rank LULAC's as likeliest to make it's way further down the process than others. Here's the nub of their argument ...
LULAC filed its legal challenge in the U.S. District Court's Western District of Texas. The suit alleges the state is trying to take away votes from Latinos.
Vera said the first issue they have is with the 2010 U.S. Census. According to Vera, the census did not provide an accurate count of Latinos in Texas. Vera argued if the count was accurate, Texas would have gained a fifth Congressional district, so the lawsuit seeks to have those numbers thrown out and an accurate count provided.
The second part of the suit alleges violations of the Voting Rights Act, specifically that Texas Republicans drawing the new maps are packing Latino voters into districts in disproportionate numbers.
LULAC also argued that as it stands now, the redistricting takes away one Latino opportunity district without replacing it with another one.
I'm not a lawyer, nor am I going to pretend to be one on a blog or television. But I don't seem to recall "bad census numbers" ever being a very successful grounds for lawsuits such as this. But the second leg of their suit should have better grounds. To the extent that I'm willing to game this out, I'd suspect that DOJ takes the most offense with the treatment of DFW minorities and the courts take the most issue with things like the CD27/CD34 swap. Depending on how CD23 measures out in terms of retrogression, I can see that one being an issue in either setting.
The reason I'd argue LULAC lawsuits are generally stronger is that they aren't as tainted by incumbent members of Congress who try to throw in partisan aspects of redistricting, which generally don't hold up in court. I'd have to review how the DFW situation of 2003 held up in court last time around. At that time, it had the double benefit of being a strong community of interest argument that went hand-in-hand with an incumbent's argument (in this case, Martin Frost). Obviously, the fracturing held up in the courthouse round at that time despite the fact that the career attorneys in DOJ found the fracturing to be out of VRA compliance. All that to say that if there's any lawsuit that expends a great deal of time trying to argue over the division of Travis County in the latest Congressional plan, I don't see it winning. It may be ugly, it may be blatantly partisan, it may be unfair as all get-out. But it's legal.
Likewise, coalition districts will be harder to defend than true, 50%-plus single-minority districts. And coalition districts that rely on Anglo voters (like Doggett's) with an overall majority Anglo population would seem to me to be out of the question unless there's an incredibly favorable selection of judges in multiple rounds of appeals.
So keep an eye on LULAC's lawsuit as it may be one of the strongest challenges in the courts to the present map.