Final answer:
An HVAC Technician is the professional who connects gas and oil lines to appliances and HVAC units.
Step-by-step explanation:
The professional who would connect the gas or oil lines that are connected to appliances and HVAC units is an HVAC Technician. A plumber may work with gas lines in some contexts, but for connections to HVAC units, you would typically require the specialized knowledge of an HVAC technician. These professionals are trained to install, maintain, and repair heating, ventilation, and air conditioning systems, which includes handling the necessary lines for gas and oil for these systems.