Yes, you are limited to AC 'destination' chargers. e.g. ones installed at home, hotels or your place of work etc. rather than rapid chargers. As you have found out, Tesco also provide some AC chargers but they aren't that useful for full EV owners as you aren't there long enough to make a significant difference to your charge level so I don't expect to see the amount of these to increase in huge numbers.
Given the battery is quite small, and you have a petrol engine to fall back on, there isn't really a need for rapid charging which is why Lexus avoids the expense of providing that functionality.