I think you're absolutely correct in that LW is unique. Being unique is actually a common part of many of these cult movements. Developing a shared language helps build unity, and the feeling that you're special. In this way, I'd compare LW to Mike Bickle's movement, International House of Prayer (IHOP). LW was even associated with them briefly in the 2000s, sending some "ambassadors" to pray with the movement and also with the likes of Todd Bentley and the Los Angeled Lakeland Revival. Gary and Marilyn actually attended a few of Bentley's services in Los Angeles at the height of his popularity before he got caught sleeping with his secretary. I can remember seeing them on television.
The IHOP movement reminds me of LW in that they have a commercial Public Relations wing that is very timid compared to their pastoral wing. IHOP has a very active Public Relations team that invites many evangelical movements to pray. However, pastors and youth leaders within IHOP are subjected to a much more rigorous lifestyle. Numerous 'offshoots' of IHOP have been identified as cults, and the church is quick to distance itself from any controversial youth leaders. Some point to the founder himself, Mike Bickle's, as a cult leader, responsible for all offshoots of IHOP. All IHOP pastors are required to memorize Mike Bickle's Prophetic History (PH), which has been amended numerous times since the 1980s due to prophesies and miracles that were disproven. Pastors are encouraged to submit to elders, live in communal homes, and they are discouraged from attending traditional colleges-- instead attending non-accredited IHOP "academies." The thought process is that college is unnecessary as "God is moving radically in the world and will soon bring miracles and true wisdom." Sound familiar?
LW structures itself in a similar way with PR ventures like the Christmas Truck, New Years parties, and the July Fireworks extravaganza. New members are discouraged from attending the School of Prophets or any services with prophesy. That all changes once a member is 'in the fold.' They are then highly encouraged to submit to church leaders and memorize JRS's own "Prophetic History."
Good article on IHOP: