Sorry to split hairs, but a government site like boosterseat.gov is NHTSA's, and not technically a lobbyist's site, although it could be influenced by lobbyists.
Lobbyists are hired to represent a company or interest group to lobby/nudge/encourage government regulators or politicians to enact policy or legislation that would be preferable for that company or interest group. The OP is asking if the carseat manufacturers employ lobbyists. I wouldn't be surprised, but I honestly don't know for certain. I don't doubt Britax's parent company, the Carlyle Group conglomerate, has a gaggle of lobbyists, but I do not know if it employs lobbyists specifically for child passenger safety advocacy. I do know carseat manufacturers themselves have some direct interaction with gov't. For example, a few years ago, the then President or CEO of Britax testified before Congress on the subject of booster seats.