It's not so much about needing the scaling solution so much as proving LTC can be agile where BTC cannot be.
If segwit can get activated within a few weeks of signaling it will be a huge boon to LTC.
Anyone that uses both coins knows the immense benefits LTC has over BTC. (Faster syncing, quicker transactions, anti-spam, larger TPS capacity)
Now we have the potential to leap frog over bitcoin as opposed to forever trailing it.