Superhydrophobicity plays a pivotal role in numerous applications. Recently, we have demonstrated the potential of auxetic metamaterials in creating superhydrophobic materials with unique wetting properties. However, the superhydrophobic properties are lost when the liquid penetrates into the surface structure. Understanding the conditions for droplet penetration is crucial for advancing wetting control. Here, we experimentally identify the transition from droplet suspension to full-penetration on an auxetic bowtie/honeycomb lattice membrane. We develop a comprehensive physical model surface representing different states of strain, ranging from auxetic to conventional lattice membranes, and consider the wetting as the liquid surface tension is varied using water/ethanol mixtures. By examining the interplay between contact angle and lattice structure, we gain valuable insights into the conditions for droplet suspension and full-penetration. Additionally, we develop a simple touch test to discern whether a droplet has effectively fully penetrated the structure, providing a practical and efficient means of distinguishing the different wetting states (suspended or partially penetrating vs fully penetrating).