Hi Jamie, thanks for the question.

Invasive plants can be hard to control.  The herbicides with active ingredients 2,4-D, MCPA, MCPP, dicamba, and triclopyr work well in controlling lesser celandine, preferably with 2 or more of these active ingredients.  Note that these can volatilize so following the label information is important. You can also spot treat with the non-specific weed killer glyphosate all though that will kill the grass whereas the other active ingredients are broad leaf killers.  Otherwise, you would need to completely dig out the plants and tubers and dispose of properly. Most likely any method will need to happen over a few years.   Timing is also critical (see article).  If near water, you may need a permit and use an appropriate aquatic formulation.  In using any pesticide, read the label. The label is the law.  Check out the following article for additional information.

Lesser Celandine: A Beautiful Plant with an Ugly Nature | BYGL (osu.edu)

I hope this is helpful.