I don't think anyone can 100% if the strikes will happen or not.
The bad news is that small, local rail is most likely to be affected. The guaranteed trains tend to be large trains that run from big city to big city and it is usually 3 in the morning and 3 at night.
As a back up I would look into other forms of transportation.
I believe there is a La Spezia to Lucca bus once or twice a day. I'm sorry I have no idea if the train strike will stall out traffic on the local CT line and prevent you from getting to La Spezia except maybe by ferry.
You also might look at a tour company or dedicated NCC driver to get you from CT to Lucca.
I have used this company: https://en.turislucca.com/ for local guides in Lucca and they also do cruise ship transportation tours. Maybe they will come pick you up in CT and then get you to Lucca along with a tour of some kind.
There are Lucca to Florence buses and then you could take the bus to Siena. As I recall there may be a once a day bus from Lucca to Siena but it was a horrible time like 7:45am. It is the most direct way but your time in Lucca will already be short and then you'll leave super early. But during a strike you may want to trade tourist time for definitely getting there.
Keep in mind that while the strike is on others will be looking to use buses and even when the strike ends and the schedule returns to normal there will be pent up demand - like you - looking to take use it.
Hopefully the train strike will not happen at all, good luck,
=Tod