I am absolutely no expert on greases, but I will give you my opinion anyway.
I question whether "fibrous" nomenclature even applies to today's modern grease. To my knowledge, fibrous grease is something that was used in the Model T days and several decades beyond that. Greases back then were described as short or long fiber based on how they looked when pulled apart. A true fibrous grease was described as being sodium, anhydrous soda, or potash soap based and VERY fibrous in appearance. I have the impression that it was for more crude bearings, it didn't release it's oils well, and was not too water resistant. Here's a decent discussion on the subject: https://www.practicalmachinist.com/vb/general/fiber-based-grease-171568/
Another discussion: http://www.mtfca.com/discus/messages/708324/712735.html?1484323687"In terms of lubricating grease, the word fiber generally refers to the interlinked molecules of soap thickener in the grease, the component that gives grease its characteristic consistency. Some manufacturers refer to the thickener as soap fibers. Some soap thickeners, especially those based on sodium and barium soaps, tend to impart a somewhat fibrous texture to the grease, while those based on calcium and lithium soaps tend to produce greases with a smoother texture. Modern greases do not contain what are typically thought of as fibrous materials such as cotton or wool
Amalie has a sodium grease they describe as highly fibrous for heavy, open bearings: http://www.amalie.com/Grease/Heavy-Duty-Wheel-Bearing-Grease
Lucas Red and Tacky is a common lithium complex grease that they describe as "smooth and tacky". I don't think tacky is the same as fibrous. R & T is certified GC-LB - good for both chassis joints and wheel bearings. Having said that, their literature markets it more as "especially good for sliding surfaces and open gears".
If I was doing high quality automotive bearings or similar, I would probably choose something marketed more for that. Just my 2 cents.
I have no experience with Lucas R&T and cannot comment how good it is for bearings. Maybe someone with actual experience will provide some real world advice.