Well, now you're going off in a COMPLETELY different direction if you are talking distances out to 300 yards. The Henry Big Boys are really cool, mostly fun guns that can be used out to 150 yards if needed. Mostly, they are a 100 yard affair in reality. They shoot big slow rounds relative to normal hunting choices.
I have a 30-30 and 45-70 lever action and I appreciate them for the throwbacks they are and they are very handy for some things. I would like to get a pistol type chambering one day.
But if you are talking about sure-enuff flat shooting 300 yard type lever actions, then as mentioned you are talking about Browning BLR territory. I have 2 of these as well, one in 7 mm mag and the other in 325 WSM. They both have good scopes and 300 yards is no problem at all for hunting. They come in calibers like 270 Win, 30-06, .308, .243, .223, 22-250, 7-08, etc as well as the cool WSM calibers. I am always looking for a good deal on another one. I would like to get a 7-08 or .243 and actually I have seen a couple in LNIB condition for around $500-600 range. But the new prices are typically around $800-900.
The Browning BLRs are really fine cool rifles and I like them a lot. But they are a totally different animal than what you started out talking about.