He's never going to get out.
The NCAA will do nothing.
Wisconsin has established the precedent that any school can prevent a transfer by simply refusing to file the paperwork.
Wisconsin's legal team will create such cost for Lucas that it will be cost prohibitive and take years for him to get out. Similar to a player challenging the NFL's three year requirement for entry.
Dangerous move that can backfire, which is part of the reason most public universities don't engage in that tactic. By example, in Wisconsin:
Under Wis. Stat. § 895.044, a party or party’s attorney may be liable for costs and fees under the section for commencing, using, or continuing an action, special proceeding, counterclaim, defense, cross complaint, or appeal which:
(a) was commenced, used, or continued in bad faith, solely for the purposes of harassing or maliciously injuring another;
(b) The party or the party’s attorney knew, or should have known, that the action, special proceeding, counterclaim, defense, cross complaint, or appeal was without any reasonable basis in law or equity and could not be supported by a good faith argument for an extension, modification, or reversal of existing law.
Wis. Stat. § 895.044(1)(a)-(b).