High-level synthesis is a mature Electronics Design Automation (EDA) technology for building hardware design in a short time. It produces automatically HDL code for FPGAs out of C/C++, bridging the gap from algorithm to hardware. Nevertheless, sometimes the QoR (Quality of Results) can be sub-optimal due to the difficulties of HLS in handling general-purpose software code. In this paper, we explore the current difficulties of HLS while synthesizing Lattice-based Post-Quantum Cryptography (PQC) algorithms. We propose code-level optimizations to overcome the limitations of high-level synthesis increasing the QoR of generated hardware. We analyzed and improved the results for the algorithms competing in the 3rd round of the NIST standardization process. We show how, starting from the original reference code submitted for the competition, original performance and resource utilization can be improved, in some cases with a speedup factor up to 200 x or an area reduction of 80%.