I downloaded your raw file, and just as you show, it looks awful in Lightroom. It's giving me a White Balance as Shot of 2600, and the reds look really pink and awful. Impossible to correct in Lightroom, too far from where they should be.
You must know, that this does nor happen, not even remotely, with Leaf files, the Leaf files look pretty close in the Leaf application versus Lightroom, and because of the incredible amount of tweaks that you can do in Lightroom, particularly with the HSL sliders, you can -in my opinion- surpass the Leaf software, or at the very least match it pretty easily, a reason why I use Lightroom "tethered" via the watched folder. I could just as easily use Leaf, but I use Lightroom because it's far faster and stable.
It could be that Phase and Lightroom aren't fined tuned yet, maybe the nature of the raw files makes it difficult to achieve, unlike other brands. Lightroom has been reading Leaf files for a long time.
Certainly, if your Phase files are representative and other Phase users are finding similar bad results, I would say Adobe shouldn't have announced compatibility (if they have), because judging only by your file, it doesn't appear to be ready yet.
As a matter of interest, what white balance is Capture1 reading. I mean 2600 is way down normal conditions. What lighting did you use?
Anyone reading might have come to the conclusion that Lightroom is really awful, when in fact, at least in my experience, it's bloody good!
PS. I just downloaded a raw Leaf file from their website (because I'm at home now and don't have my own here). Opened it in Leaf C11.1, and it looks very good. I chose the file with vegetables and red apples, oranges, since your problem is mainly with the reds. Perfect in every colour.
Then I opened it in Lightroom, absolutely perfect too. Just for your info.