SINCE the 1940s, southern California has had a reputation for smog. Things are not as bad as once they were but, according to the American Lung Association.

but 用在此处毫无道理。句子似乎没有结束，but 后面肯定还有一个并列分句，according to the American Lung Association 是个插入成分，前后应该是逗号。

原句结构应该是这个样子：

Things are not as bad as once they were （第一并列分句）but, according to the American Lung Association，+ 第二并列分句。

but 之前是个含有比较从句的主从句：Things are not as bad as once they were.

意思是： 现在的情况不像以前那么糟。