Okay.
First of all, correlation is not causation. If there is actual evidence that Lasix CAUSES unsoundness I would like to see it. There have been plenty of changes in racing over the years, including a far higher percentage of foals coming from commercial breeders, as opposed to those who breed to race, and have more of an interest in soundness. And racehorses are also much faster (see Archives this site), which places far more stress on bone and ligament. Are major league pitchers using Lasix? Because you ain't gonna be seeing anybody starting their career now win 300 games, let alone 511.
The "masking agent" thing was kicked around for a while, I haven't heard that one for at least 5 years.
Big picture-- even if it were true that Lasix use was against the welfare of the horses (all evidence is that exactly the opposite is true), welfare of the horses is not the only consideration. If it were we wouldn't race horses at all. The welfare of bettors, who will be facing increased randomness (remember synthetics?) and betting against more "smart" money based on inside information, is at stake. And ultimately, that means the welfare of the industry is as well.
And that's not just about the bettors. The economics for owners are bad enough already, and it is already hard enough to fill races. Owners will leave the game over this.
One more thing. As Curtis hinted at, anyone who thinks getting into bed with PETA will appease them is a fool. When that 1/5 shot bleeds because he didn't get Lasix they won't be screaming to allow him to get it. They will be screaming to ban racing.
As for the differences with American racing-- I can think of a couple of differences right away. First, the pace is almost always far hotter here than in Europe, they are stressed all the way, which is why they are almost always decelerating the last half of the race. Second, most tracks and training facilities here are in or near urban areas, air quality might be different.