Fastest route to 99 lives in Super Mario World
Solution 1:
Assuming you want to get 99 lives as fast as possible from a fresh start, I believe the optimal solution is not to race to later levels but to spam Yoshi's Island 2, where you can quickly get several extra lives by using the Koopa shell near the start. Just throw it at the line of Koopa Troopas and run after it to keep it on screen. If done correctly, you should be able to get five extra lives within 15 seconds of starting the level (probably even slightly less, but I can't test it right now). Since you start with 4 lives, repeating this process 19 times should suffice.
You have to complete the level once, after which you can exit the level midway after gaining the lives. Assuming each attempt takes about 15 seconds, plus maybe additional 30 seconds for finishing the level for the first time, you'll be packing 99 lives in about five minutes fifteen seconds from a fresh start.
(it is also possible to use a glitch in Yoshi's Island 2 to inject arbitrary code in the game (video), including the possibility to add any amount of lives but since it's both insanely difficult and likely to be considered bad sport I'll leave it as a footnote)
Solution 2:
I think the fastest way is grey coins in Vanilla Secret 2. Get the gray P button near the Spinys, hit the button at the beginning of the level, collect the grey coins, gain a lot of lives. This isn't too far into the game. I would argue that if you take the lake path instead of the cave path in Donut Plains, you could finish it in well under 15 minutes, possibly even under 10.
Solution 3:
Vanilla Secret 2, but just jump on the koopa paratroopas back and forth with the cape equipped. Don't use Yoshi because he'll destroy them. Jump on the paratroopas and regular koopas, but do not land on the shells or shellless koopas and the regular koopas should respawn as you go back and forth. It's 1up per jump but its more involved, requires less travelling and restarting, and you can finish off by grabbing the silver coin trick near the end of the level with the pswitch and spinies to get an extra 6 lives.