I'll toss in some feedback. Feel free to pass it on. New Mexico Lottery website is terrible. Not all the games are shown on the homepage. Worse, the constantly changing scrolling game information. Maybe it works better on a mobile phone? Don't know, but probably not. Take a look at some other state lottery websites for ideas.
As for games, NM Lottery doesn't have a Pick-4 game? As for Pick-3, it may not seem exciting compared to other games offered, but it's a relatively large, reliable revenue driver for many lotteries. Pick-4 would be a good addition. If NM Lottery is concerned about prize funding, maybe partnering up with another lottery for Pick-4. It appears some other U.S. lotteries do that.
As for claiming winners. NM Lottery 90 days is downright awful for players. Probably the shortest claim period of any lottery in the U.S. It's as if NM Lottery doesn't want to pay out prizes; hoping winners miss the deadline. Ohio Lottery 180 days isn't great, but similar to that of many other lotteries. 1 year is better, and better accommodates players who frequently travel. Also, a longer claim deadline, such as 1 year, allows for easier selling of advanced play tickets 13-26 weeks ahead.
Ohio Lottery website, while not spectacular, is usable. More to the point, OH Lottery has a decent numbers and instant game mix already.
Though, the OH MyLotto Rewards may not be overly productive for multiple reasons. Firstly, the entry of tickets can highlight to players how much they're losing. Second, many players want to win more, not "buy" trinkets of marginal value. Thirdly, regular, higher wager players will feel, rightly so, they're getting ripped off due to entries being limited to 1200 points (equivalent of few as 60 $20 instant tickets over an entire month) verses no limit for some other states that offer second chance entries; often for cash prizes verses buying items.
Hope this helps.