Assuming any particular vehicle can get additional power out of higher octane fuel the benefits will not show them selves immediately. Vehicles do not have any direct way to analyze the octane rating of the fuel. The ECU will adjust timing over time until the pre-nock sensor detects pre-detonation at which time it will back off some and begin the process again. So if you have been running 87 octane and then change to a higher octane it may take a few tanks of gas for your vehicle to adjust. This is assuming that the vehicle is capable of getting any benefit from higher octane fuel which is influenced by engine design, temperature, air density and probably other factors. Additionally, altitude (air density) has an impact on timing which is why mountain states (free states) in the US typically offer lower octant fuels (85 octane).
When we were in the Black Hills of SD and throughout MT and WY (up into Yellowstone and Grand Teton) last month I ran either 87 or 91, depending on what the lowest octane at/above 87 was available, even though 85 was available. I'll second Markuson's comment that I didn't notice any difference in fuel economy, power, etc. In fact, I still got better mileage in IL/WI on 87 near sea level than I got on 87 at ~5000', even on flat roads. Obviously this is all anecdotal - the scientific way to test would be to run the same roads under the same conditions (temperature, wind, etc) numerous times but I'm unlikely to make that trip more than once per year

Going back to the original OP, my financial self says run 87 in an LC as there's little if any difference in performance but a significant difference in cost. In an LX you can decide what to run - if you run 87 the vehicle will adjust the timing so you'll lose a little power, but given the available HP and torque the LC and LX have you probably won't care for most normal driving. The only way low octane will cause an issue if if it's so low that the ECU can't retard the timing sufficiently. You won't see that on 87 but maybe you'd see it if you filled up with 85 in the mountains and then drove at sea level on that tank (or maybe you'd need to run an even lower octane). More importantly than octane, try to buy top tier gas when its available.