Efficient Virtual Machine (VM) migration is pivotal for optimizing resource utilization, ensuring SLA compliance, and minimizing operational costs in dynamic cloud environments. However, existing strategies often lack theoretical rigor, ignore dynamic cost-performance trade-offs, or fail to guarantee convergence to stable placements. This paper introduces VMigrate+, a novel SLA-aware and cost-optimized VM migration framework grounded in lattice-theoretic optimization and constrained utility maximization. VM placement states are modeled as elements in a partially ordered lattice, and migration decisions are driven by a monotonic utility function that guides the system toward Pareto-optimal configurations. The framework integrates stochastic cost modeling, SLA violation bounds derived via a Hoeffding-type concentration inequality with rolling-window performance estimation, and a Lagrangian-based constraint handling mechanism to respect budget, capacity, and migration-frequency limits. We formally prove the existence of utility-maximizing fixed points and show convergence under Lyapunov stability conditions. Extensive CloudSim-based simulations demonstrate that VMigrate+ reduces cumulative migration cost by up to 25.6%, decreases SLA violation probability by 46.2%, and improves average utility scores by 7.5% compared to baseline methods.