I've heard through a semi-reliable source that it's all about the money. Lawson brings in quite a bit more than Tsunoda. This was a big reason Checko was able to hang on so long.
But yeah, Lawson's likely on a short leash.
The idea that Lawson brings in more cash than Yuki is interesting and appears unlikely. His helmet carries a Zuru logo (which looks like a former NZ toy brand now headquartered in China), but his webpage lists mainly smaller NZ industry sponsors (a local car dealership group (Giltrap), construction equipment suppliers (Porters) etc), that pale in comparison to multinationals like Honda, Marina Bay Sands, financial services/brokerages XM Trading & GMG Brokers, and others backing Yuki (bottom of the page).
In the end, you're right that money played a part based on rumors RBR came back to Honda asking for the money that was on offer last year to swap him back in for Japan.