Not necessarily.
Dealing with Nagalim doesn’t require sending funds from a specific (registered) address.
To exchange with Nagalim, you may withdraw from the exchange to Nagalim’s address and receive funds in turn on your exchange address.
Using NuLagoon to balance funds on exchange requires moving them through wallets.
Only if you have sufficient funds in the wallet and can balance exchange funds with that, you are as fast as when dealing with Nagalim.
The benefit of not having to make a deal with NuLagoon, because everything is automated, remains.
There are cases in which NuLagoon works better.
In other cases Nagalim wins.
It’s not only about the spread and the fee.