Well, yes and no. Technically, based on a decision last year by the head of the Library of Congress, it is illegal to unlock your phone without the carrier's permission. But neither the Library of Congress nor the FCC have a police force, and the FBI isn't going to go looking for people who have illegally unlocked their phones.
And Sprint and Verizon phones do roam on each others networks. It's possible, if you're rooted, to load a PRL on your Sprint phone that forces it onto Verizon's network, and I suspect the reverse is true as well. But you'd still be a Verizon customer, paying your bill to Verizon, and probably getting your account cancelled for roaming too much. It is probably possible to root your phone, and change the IMEI and MSL to something that would work on Sprint's network, but no one here will tell you how to do it even if they know (I don't), it wouldn't be easy, you wouldn't get 4g, it would be a violation of the terms of service, and if you got caught they'd probably cancel your account.
Easier answer: sell the Verizon phone on ebay or Craigslist, and buy a new or used one for Sprint.