The thicker copper pipe, as you correctly named it: suction line, is the only one that requires insulation because it carries low temperature, low pressure gas from the coil inside the house to the compressor on the exterior.
Lack of insulation would cause a lot a condensation and significant energy loss. The thinner line transfers high temperature, high pressure liquid gas from the compressor to the coil located inside the air handler.
Since it operates in already high ambient temperature, there’s no loss of energy (insignificant if any), and insulating is not necessary. An exeption would be if they travel through some areas where the surrounding air temperature is higher than 110°F - that's their approximate temperature (like attic), in which case insulation installation is recommended.
To “hide” your ac lines from… those people, you can use specially designed for such purpose “line set cover” (read my answer below). Let me know if there’s anything else I can help you with.