The bad news: Removing lesser celandine is difficult. In addition to its wide spread once established, removing the plants entails fully digging out the roots. Just cutting back the tops will not restrict its return. Even for people inclined to use chemicals, there’s aren’t really any good options.
Your best option is to invest the time in spring to remove the weed and keep at it for a couple years. Our crews have observed that a full removal in spring leads to about a 60% reduction in the return the following year and similar progress in years to follow. Like any invasive, persistence is required but pays off in the long run.