You probably already heard this:  For longevity (if you plan to keep the vehicle for as long as possible with minimal issues), I would pick the Lexus ES350 despite the higher mileage.  The Acura ILX comes with a naturally aspirated 2.4L I4 engine with direct injection only (which means it is susceptible to carbon build up over time on back of intake valves, so need catch can to mitigate - one more maintenance item - but you might still have to periodically clean the back of the intake valves every so often) - the engine overall is fairly good, but the deal breaker is it is mated to an 8-speed dual-clutch transmission only.  For longevity and lower cost of ownership (you didn’t say how many years and miles it needs to last you) it’s better to go with a regular automatic transmission (the Lexus has the 6-speed AT) since the dual-clutch can be very expensive to repair/replace if/when it has issues.  Also, the Lexus comes with naturally aspirated engine 3.5L V6 (also true and tried).  But the nice thing is that engine comes with both port and direct injection (clever system) and the port injection portion manages to spray gasoline on the back of the intake valves thereby cleaning the gunk off.  Between the two, and if you plan to keep for a long time, no question the Lexus has a better chance to last longer even though the Acura might be more fun to driver.