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A nursery pot is a training pot.
We’ve a couple lilacs here, including hardy dwarfs like Miss Kim. As bonsai, they are interesting and a bit finicky
Personally, I’d get the next size larger nursery pot, cut it down 1/2 way and slip it into there for this year and ….maybe even next, depending upon your success in keeping the tree healthy.
The first thing I’d recommend is figure out how tall and what style you want this tree to be. This will guide everything beyond.
Selecting potential branches now would be ok. Keep in mind that whatever you do the tree must be robust enough to get through the winter. So cut back and do follow up care with this in mind.
Generally in my experience lilacs like to be kept moist, not wet, at all times.
Also please double click your icon on the top of the page and enter your approximate location and the USDA plant hardiness zone. This information will follow you around on each post so we can quickly tailor our assistance based upon this data. It will also key others in your area to respond.
Welcome Aboard once again!
cheers
DSD sends