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We consider several object sharing synchronization mechanisms including lock-based, lock-free, and wait-free sharing for LNREF , an optimal real-time scheduling algorithm on multiprocessors. We derive LNREF's minimum-required space cost for wait-free synchronization using the space-optimal wait-free algorithm. We then establish the feasibility conditions for lock-free and lock-based sharing under LNREF, and the concomitant tradeoffs. While the tradeoff between wait-free versus the other sharing is obvious, i.e., space and time costs, we show that the tradeoff between lock-free and lock-based sharing for LNREF hinges on the cost of the lock-free retry, blocking time under lock-based. Finally, we numerically evaluate lock-free and lock-based sharing for LNREF.