Does a Venomthrope gets an extra attack for using multiple weapons?
The reason why the entry for Venomthropes does not list off "two pairs of scything talons" is because Venomthropes--unlike Raveners--have options for how to arm up that are zero cost.

Looking at the Fast Attack Ravener Brood entry, it lists under options:


  Any Ravener may exchange one pair of scything talons for rending
  claws - 5 pts/model


In other words, a Ravener will have two pairs of scything talons--all the time--unless you pay 5 pts/model to switch it out, using this optional upgrade.

Let's focus on the Designer's Note you referenced:


  Designer’s Note: Tyranid Melee weapons come as pairs. For game
  purposes, each pair is treated as a single Melee weapon. This means
  that Tyranid models must fight with two pairs of any Tyranid Melee
  weapons to gain a bonus Attack in close combat for fighting with two
  weapons. For example, a Hormagaunt armed with a single pair of
  scything talons does not gain a bonus Attack, but a Ravener with two
  pairs of scything talons, or a Genestealer with a pair of rending
  claws and a pair of scything talons, does.


If your model has four (4) lash whips, that is very straightforwardly two pairs of weapons.  Each pair is treated as a single melee weapon.  Your model therefore has two melee weapons and will gain a bonus attack in close combat for fighting with two weapons.

Or put another way:


set aside two lash whip models.  two bits, one pair, for game purposes single melee weapon.
set aside two lash whip models.  two bits, one pair, for game purposes single melee weapon.
does the venomthrope support holding all of the physical weapon bits?  If the venomthrope has all four weapon bits, the venomthrope has two melee weapons.


So in a normal assault-phase attack (non-charge), you would get 3 attacks: 2 (base attack score) +1 (double melee weaps)