What should the succession term in the LPA read, be stated?
It's not necessary to have one. This is typically handled at the ManCo level, not the fund. Also, see the Limited Operations Mode in the cornerstone LPA, downloadable here, which states:
Limited Operations Mode. In the event the Limited Partners claim there exists a Material Breach, Limited Partners holding more than 66 ⅔% of the aggregate Commitment Percentages held by all Limited Partners (“Requisite Majority”) may cause the Fund and General Partner to enter into “Limited Operations Mode.” The period of Limited Operations Mode shall commence at the time that a Requisite Majority provides written notice to General Partner particularizing the facts constituting a Material Breach and ending automatically on the date ninety (90) days later, which period may be extended by successive ninety (90) day periods if, and only if, a Requisite Majority provides written notice extending such period. During Limited Operations Mode General Partner and the Limited Partners will negotiate in good faith to resolve the dispute.