Actually the luck bit on neo tends to have more to do with sticktoitiveness than actual luck, because the 'luck' comes with more activity.
Tips to 'luck':
Play javascript games to dramatically increase your RE's (neggsweeper, dice a roo, neoquest, double or nothing, etc.)
With stocks, just max out the amount you can buy everday, never buy shares over 16np, and over time what has gone down goes up (you can't go wrong if you have patience that endures for 6+ months)
Enter contests found on the Pet Central page. Clever ideas + time and effort will get you a win eventually, and many of the contests offer nice prizes.
Make friends, be generous and helpful to them and most will return the kindness in many ways.
Keep a log of things you win/experience, because you are definitely getting more than you think. I keep a neopets blog just for this purpose (qbureau.wordpress.com). Even now I will swear to my friends I rarely get any good changes from the lab ray, but a quick review of my blog points out my perception is way off. Actually, if you want to see how Adee chases me with her dumb random events, type 'adee' into my searchbar and view my Adee-induced insanity
Revaluate your goals on neopets; do you even have any. Aimlessness always leads to dissatisfaction. If luck is your focus, then you're in the same unlucky boat the rest of us are in and only playing more can increase your so called luck. Luck is a gamble, and therefore only fun if you're coming out ahead. There are tons more things to do on neo that will gain you a lot more than sitting around waiting for something exciting to pop up out of nowhere.
Actually, think of the 'luck' as a percentage of the time you give to neopets. If you play a couple flash games and chat on the boards for a bit, you will be 'unlucky'. If you go for gold in neoquest, work on projects like lookup and petpet pages, help your friends and random people, try and learn something new like how to restock, etc., then you will become shockingly 'lucky'.