In front of the cameras, they seem to have a nice chemistry, even the Yoshimoto Kogyo members from Kansai with those from the Kanto area. They appear in other programs together as well, so I don't think it's a matter of rivalry between them. Unlike Gaki, the focus was still on Downtown, but the work of the other members were usually highlighted.
Gaki has that "je ne sais quoi" chemistry that works. Probably because they've been together for so long. For Lincoln, I feel like Downtown, Summers, and Miyasako had good chemistry. Not quite with the rest. They're fine when everyone's participating equally, but when it comes to free flowing interaction, I feel like the others either couldn't keep up or deferred to the older guys (Miyasako being the exception). It's not that they didn't like each other on camera. But they never reached that high level of chemistry that makes a segment where they're just driving around in a car consistently get more than 10% ratings.
Also, my feeling is that other shows that have been doing well have a focused purpose, are more topical, and definitely get young tarento as well as non-comedians on to interact with comedians. Lincoln was sort of "traditional variety" in that their goal was to do "regular" funny things on TV and most of the guests they invited were just other comedians. Perhaps this is considered kind of stale in Japan nowadays. Non-comedians interacting with comedians definitely feels different and can feel very fresh compared to comedians interacting with comedians.