Paper applications didn't have a per QSO fee except after the first 120 QSOs.
The new fee structure for paper applications is now 15 cents per QSO for everything over 101 QSOs.
And it's 8 cents for online apps.
Point still stands, LoTW apps are more likely to net more in fees.
Let's say you have 101 QSOs. Here are the fees (excluding certificates and shipping):
LoTW: $5 + 101x$0.12 = $17.12
Paper: $15 (101 QSOs free)
Online: $7.50 (101 QSOs free)
LoTW brings in $2.12 more in fees than paper and almost $10 more in fees than an online app. As for the margin, I have no idea what it costs ARRL to process each of these apps but given that the DXCC staff is likely salaried and not hourly and the LoTW servers cost about the same amount to run whether or not people are submitting LoTW apps, those are fixed costs.
Also AB8MA's point is a good one. With LoTW I usually just submit all the credits I have instead of cherry picking for awards. Since LoTW is automatic I get more of these than I do actual QSL cards. So even more in fees is sent per app as a result.
I don't really care about how much ARRL "profits" from it as I'd rather see the league get the money but make no mistake, LoTW does indeed bring home the bacon.