This came up in another whip thread, but the weird thing about grappling with a flexible reach weapon like a whip or lasso is, while one can picture wrapping the whip around a target to prevent them from getting away, there's nothing to prevent the target from coming toward you. They're not truly grappled, then, since in one direction their speed is not zero. You almost need another condition, like Roped, or have to spell out the exact effect in the weapon description, without referring to existing conditions.
If you want to truly grapple with a reach weapon, stat up a mancatcher. (Two-handed, probably does damage if you put spikes inside, but always has with disadvantage on attacks without a feat.)
I think I would allow tripping with a whip, but, as per the Shove attack action, it's in place of a regular attack. So no weapon damage included. I'd also have the attacker use their normal attack roll, since it's still with a weapon, instead of Str (Athletics) for the contested roll. This prevents any Expertise shenanigans from a rogue, even with lower Strength.
Again, to avoid having to add caveats, it might just be better to spell it out as two specific types of contests, and not even bring the existing contests of Shove and Grapple (and the Grappled condition) into it.
One interesting side-note, the Battle Master has a Tripping maneuver, which is only resisted by Strength, (not Strength [Athletics], and not by Dexterity at all).