Because the Lexus/Toyota setup ISN'T designed to be a true electric vehicle(EV) hybrid set-up. It's essentially a normal petrol car, hence the engine is on most of the time. The EV element of the IS300H is designed to recapture energy lost in braking, and than use that energy to provide 'limited' EV power to help supplement the main engine or provide very limited electric only running. The EV battery on the IS300H is only 1.9 kWh, and only 1.5 kWh is usable, this is a tiny battery compared to a even a Mitsubishi PHEV, which has a 12 kWh battery.
Essentially there are now several 'grades' of EV/Hybrid cars, though they are all called hybrids its confusion.
1: Toyota/Lexus/Infiniti hybrid drive units = These really are just ICE (internal combustion engine) units, where the 'hybrid' bit is only really to recapture lost brake energy, allow the ICE unit to run very efficently, and provide very 'limited' electric vehicle (EV) running, about 5 miles. Because of the small battery (<2 kWh) they don't need to be 'plugged in'. The battery in the Lexus is small enough to sit under the boot area without impacting on storage space.
2: Plug-In hybrids (Golf GTE/A3 Etron/ Mitsubishi PHEV / BMW i8) = These cars have a proper ICE unit, and a decent battery size (6-12 kWh). As an result they can work as a pure electric car for 20-30 miles, before electricity runs out and they need switch to ICE power. Because of the much larger battery they need 'plugging in' to fully charge the battery. However because they have to carry both a fully functioning ICE unit and large battery these things are heavy. These larger batteries need to be integrated into the drivetrain better to stop the boot space from been swallowed up. Both the GTE/A3 have tiny boots because the battery packs weren't designed to be integrated it the drive train unlike the Mitsubishi PHEV.
3: EV cars with ICE units as 'range extenders' ( i3, Ampera) = These are 'proper' EVs. They are purely powered by an electric motor, and have large batteries (16-24 kWh). However because people worry about 'range anxiety' these cars also come with a SMALL ICE electric generator. The ICE provides no motion (unlike PHEVs), and only serve to provide battery re-charging 'on-the-go'. Like all EVs you need to plug these things in, and the batteries are getting very big now.
4: Proper Battery EVs (Leaf/Zoe/Tesla) = These are pure battery powered, with no way of generating electricity on board. If you run out of charge, your stuck. Hence they have big batteries (up to 85kWh), but because they have no ICE drivetrain at all, some weight is saved. These things are basically battery packs with motors and wheels stuck on....Just like Tandy remote control cars I built as a kid, but sadly about x100 more expensive .
So to answer your question....There is nothing wrong with your Lexus, its performing as it was designed (Our 2015 IS300H does exactly as you describe). If your after a 'proper' EV driving experience you have to look else where :)