Large language models (LLMs) demonstrate outstanding capability in understanding natural language and show great potential in open-domain travel planning. However, when confronted with multi-constraint itineraries, personalized recommendations, and scenarios requiring rigorous external information validation, pure LLM-based approaches lack rigorous planning ability and fine-grained personalization. To address these gaps, we propose the Symbolic LoRA Travel Planner (SLTP) framework—an agent architecture that combines a two-stage symbol-rule LoRA fine-tuning pipeline with a user multi-option heuristic tree search (MHTS) planner. SLTP decomposes the entire process of transforming natural language into executable code into two specialized, sequential LoRA experts: the first maps natural-language queries to symbolic constraints with high fidelity; the second compiles symbolic constraints into executable Python planning code. After reflective verification, the generated code serves as constraints and heuristic rules for an MHTS planner that preserves diversified top-K candidate itineraries and uses pruning plus heuristic strategies to maintain search-time performance. To overcome the scarcity of high-quality intermediate symbolic data, we adopt a teacher–student distillation approach: a strong teacher model generates high-fidelity symbolic constraints and executable code, which we use as hard targets to distill knowledge into an 8B-parameter Qwen3-8B student model via two-stage LoRA. On the ChinaTravel benchmark, SLTP using an 8B student achieves performance comparable to or surpassing that of other methods built on DeepSeek-V3 or GPT-4o as a backbone.