Because bribing is paying someone to breach their public duty, whereas lobbying only theoretically involves you trying to persuade your representative. Sure, it can involve "bad" stuff (eg. relaxing environmental regulations), but can also involve "good" stuff (eg. relaxing zoning regulations). Citizens, or groups of citizens (eg. corporations) engaging with their representatives is part of the democratic process.
That's the pretty way to present it.
In practice, "Citizens, or groups of citizens" is true but unfortunately vague, sort of similar to "Mammals, or groups of mammals, are known to sometimes build buildings out of prefabricated concrete."
Lobbying is a heavily professionalized activity, mostly undertaken by specialist lawyers employed full-time for the job.
This is also backdoor bribery: "help us out, you got a cushy job waiting for you in the future."
So you only object to the fact that lobbying is done by specialists rather than laypersons?
2. is your argument that lobbying should be banned because almost exclusively enjoyed by the well-resourced and/or powerful? I'm not sure that's a very persuasive argument. We ban speeding because it's harmful, not because the rich are well-resourced and/or powerful to afford fast cars.
The entire content of what I want to convey here is contained in the comment you're replying to.
I think the difference is quid pro quo plus the transfer of things of value that does not conform to existing rules.
I didn't intend to say "well it could also be used for good so we should keep it legal", but yeah this is probably the better take. A better analogy might be: it's totally legal to persuade a judge of your case (ie. what the prosecution/plaintiff/defense does), and totally part of the legal process, but persuading a judge via bribes is illegal.