Lead paint poisoning? Is this a thing?

Lead paint poisoning is definitely a thing and there are warnings online about lead in Victorian and Edwardian homes. I lived in one and did a lot of stripping down but I doubt the paint was that old.
The other place it is sometimes found is in old bedsteads.
Lead paint has been illegal for a long time so you are looking at real antiques.
There is a government site giving advice about lead in old homes.
www.gov.uk/government/publications/advice-on-lead-paint-in-older-homes
I haven't read it but hopefully it is helpful.

www.independent.co.uk/life-style/tip-of-the-week-dealing-with-lead-paint-1191169.html

You used to be able to buy a test kit for lead in paint, but if there is lead paint in the house then a qualified contractor should be hire to do the work.

Old houses often had lead water pipes, with getting those checked out if you’re worried.

All paints and varnishes should be treated with great caution so I can understand her worry. If she is in a house that needs work she could research non harmful paints and varnishes. We've used lime and clay paints.Instead of varnishes we used a mix of linseed oil and spirit.

She should not be exposing herself or children to dusts of any paints and varnishes.plastic sheeting and using a vacuum to instantly remove dust is very important.

Why did you have to break the lock? Lead poisoning isn't an instant thing that would make her unable to open the door, it is cumulative.

I think she broke lockdown rather than a lock Elegran. While lead poisoning is a thing it also sounds as though the poor DD is not well. Very stressed. It's good that the OP is there to help and reassure.

The old lead paint is very durable and if the house has never been renovated it could still be present, or painted over, as your daughter is seriously concerned wash down the area where the dust is and paint the door to cover any old paint.

Lead poisoning is cumulative, which is why lead was removed from petrol, where ever the lead is you would have to ingest it to harm you.

If it was a home I was happy in,
I would do my best to replace the offending items.
Which would in my opinion be cheaper than moving home.
Not sure if the house is in a terrace or a fair distance from the main water main.
Could start by replacing the doors,and maybe at the time replace the wooden frames of the doors and possible the "wooden"? skirting boards.
I think the lead paint in the wood is only a problem when the wood starts being scraped
Ref the lead in water maybe replace the lead piping from the door step to the rest of the pipes in the house.
I think you could ask the local water authority for a quote to replace the lead pipe from the door step to where the main water pipe is in the street,although I don't think its a cheap option.
Water in general,run the water off first thing in the morning.
Fill up the kettle last thing at night,and maybe resort to buying bottled water for the family in general.
All the best and good luck.