Lesser Celandine is best thrown out to reduce the risk of it spreading further, though if sent to an industrial composting facility (one that processes large amounts of compost and can guarantee the pile will get hot enough to kill pests and weeds), that might suffice. Lesser Celandine primarily reproduces by small bulblets that easily can break off and form a new plant and which may survive backyard composting piles unless they're maintained in a way that keeps the process active and temperatures hot. Given how hard this weed can be to eradicate once it gets established, plus how widespread it's become in natural areas, we don't think it's worth the risk of trying to compost the debris and suggest putting it in landfill-bound trash collection instead.

Miri

No, unfortunately Extension doesn't have that information so don't have a jurisdiction list to share. You can inquire with your local municipal waste facility (local landfill), as several have composting capabilities. Since they receive who-knows-what in the compost-bound and yard waste material from residents across the county, they almost certainly process it industrially to make sure it gets hot and kills problem organisms like plant pests, plant pathogens, and human pathogens (such as if dog waste contaminated grass clippings or leaf litter collected by the county). Even so, the facility may ask that invasive plant material be landfill-bound instead, so you'll have to see what they suggest.

We don't have information about the waste stream processing to know what gets incinerated versus simply entombed (or perhaps both). You could ask the facility (or county government) about that also if you're curious how items are processed once they reach the landfill.

Miri