The vibrant purple, blue, and black pocket square can be paired with several suit colors, depending on the desired look. 
Here are some excellent options: 
   
Navy Blue: A classic and versatile choice, a navy blue suit provides a sophisticated backdrop that allows the blue and purple tones in the pocket square to stand out elegantly.  
Charcoal Gray: Gray suits, particularly darker charcoal shades, offer a neutral canvas that pairs well with almost any color, including the bold lavender and blue of your pocket square.  
Tan or Beige: For daytime events or a more relaxed, casual vibe, a warm tan or beige suit complements the softness of the lavender and blue, creating a harmonious and inviting look.  
Light Blue: A light blue suit can create a playful and cheerful ensemble, working well with the blue elements in the pocket square for a modern, fashion-forward appearance.  
Brown: A brown suit can work well, especially when paired with a lilac shirt to create an appealing analogous color scheme.
When styling, ensure you pull one of the colors from the pocket square (like a shade of blue or purple) into your tie or shirt to create a cohesive and polished look.