Being in the forest I have my share of lilies reaching for the sun as well. I have noticed a lot of difference between cultivars and some are very well behaved, growing straight up, while others need staking from an early age. Yes, more sun will help, specifically it's better with sun from all angles, not just one direction, so plant away from trees or solid fences and so on (if you have the option.) Also more space between the bulbs will help, don't crowd them.
If you at planting time put down a small stake close to the bulb, it can be replaced with a big later on, without fear of spearing the bulb