School me some knowledge, please. I await your esteemed tutelage, which may or may not involve waving what appears to be an acacia branch or perhaps a small pine tree over me while you wear a long white robe paired with a really big "bride of Frankenstein" haircut. Ok, just pass the Kool-Aid.
You'll have to settle for bowing to the kitsune guarding my house.
Friction and rolling resistance are two separate things. In the simplest terms, rolling resistance is how hot the tire runs (how much energy the tire uses) while friction (traction) is how much shear force is required to have the tire lose contact with the road surface. As tire technology advances--and the book we can write about what is not known about tires is far larger than the book that can be written about what is known--there is more separation between the functions of a tire vs. the parts of a tire.
A short history: In the days of bias-ply tires there was hardly any separation of functions vs. parts of the tire. Any force that acted on the tread also acted on the sidewall and vice versa. Then radial tires came along and they separated the ability of the tire to carry load and provide cushioning from the tread that provided traction and stability. The result of doing this was that rolling resistance went down a significant amount and traction went up along with tread life and flat resistance. The cushioning ability of the tire was improved as well. Looking at a radar graph of the two types of tires you'd see that every category went up. (The radar graph is larger in total area (radius), as opposed to just being larger in one or two categories and smaller in other categories with the same area.) Ideally, tires should be made with the graph being almost circular. However, there is a ways to go, so every tire is a compromise of various qualities.
Example of radar graph (no particular meaning, just the first reasonable one I found):
The first generation of low rolling resistance tires basically traded traction for rolling resistance so the area of the radar graph stayed the same--some of them were pretty slippery. The latest low rolling resistance tires have silica based tread compounds that reduce the energy used without sacrificing traction. A radar graph of these tires is going to be larger in area than the previous generation. Performance tires will make the traction radius of the graph large but reduce other radii (energy use and tread life).
Bottom line is that there's no violation of any physics here. Just improvements--and every so often a very large improvement is made so that the area of the radar graph gets larger.
So will low rolling resistance tires have as much traction as performance tires? Of course not, performance tires have given up things to get more traction--this will always be the case. Will they have as much traction as folks expect in regular non-LRR tires? In most cases, yes. The actual answer for a particular tire depends upon how the tire manufacturer tuned that tire and what tire it's being compared against. However, what you'll likely notice is that the non-LRR tires are the older tires that will eventually go away, and are really still there to provide a lower price point.