If you need a Septic System inspection I would contact Jan with Rainbow Septic. They provide excellent service and reasonable prices. They have worked in the Lake Travis and Austin area for many many years.
While there are some homes around Lake Travis and Lakeway that do have septic systems, the majority of Lakeway proper is on city water and city sewer. Septic systems are more common in Apache Shores on the east side of RR620. Generally only the older homes built before 1960 may have septic. Sometimes homes in more remote areas of the lake will have a septic system. The home seller should be able to tell you if there is a septic and if it needs work they should note that in the sellers disclosure if they are aware of it.
It should not cause undue concern as LCRA monitors the systems that are lakefront. When ever you buy a home with a septic you should simply have it inspected by a reputable company. They can work flawlessly for many years with proper care.