Generally speaking, companies are able to disguise such activities through their memberships in other trade associations, which may or may not have staff lobbyists (if not, the associations hire K Street lobbyists, which even further masks their activities).
I showed above in #28 that the American Meat Institute - which has several hundred small and mega-big members including Tyson, Cargill, etc, and claims to represent more than 70 percent of America's meat production - does immigration advocacy in Congressional Quarterly, which is certainly a Beltway "insider" publication. And if AMI sends a lobbyist to the Hill, that lobbyist most definitely has the interests of Hormel, Tyson, Cargill, et al on his agenda.
Then you see that the National Council of Chain Restaurants also works with AMI. NCCR has Mcdonalds, BK, Yum, and many others as its members (I vaguely recall their assertion that they represented "6 million restaurant workers"). Thus Mcdonalds doesn't need to send out lobbyists or do issue advocacy, since NCCR does that work for them and provides necessary cover.
So the idea is that the companies can and DO mask their advocacy programs within business associations and second- and thired-removed lobbyists.
Whether in DC or in Arkansas, they don't want their names directly attached to contoversial issues.
Alot of this can be loosely tracked through very tedious work in the opensecrets.org database of lobbyist reports, but those are designed to allow a certain amount of "slop" in favor of lobbyists, elected (and appointed) officials, and their "clients" (aka "patrons").
The alleged lobbying in this case was about “Arkansas anti-immigration legislation”, so these probably would not be K-Street lobbyists. My understanding of Arkansas disclosure laws is that local lobbyists must disclose their clients. Tyson’s lobbyist does show up on the registration list, but no registrations are shown for LULAC, McGrew or Cervantes.
The point is - if McGrew admits in a deposition that he engaged in lobbying - but he didn’t register as a lobbyist - it could be a problem for McGrew and LULAC. That may be what the plaintiffs are looking for. Otherwise, I don’t see the legal relevance of lobbying activity with respect to this lawsuit.