Yes, teal and lime green go together, and you can have a neutral in there too for a happy mix. The photo might not read very true, but I think the wall color looks too yellow for the teal and lime combo...it needs to be gray or griege or a very neutral beige. That aside, the surefire way to bring teal and lime together is to find a pillow or other textiles for the space (area rug?) that have greens and blues in them together. You are currently "processing" each of the colors individually, and nothing is bringing them all together. Lots of fabrics are out there to do this integration. Perhaps new panels in a geometric or print with these colors can bring it together? The WT looks out of synch with the modern chair.