WEEE

This is concerned with keeping electrical and electronic products out of landfill. Lamps come under Category 5, and have been included since 2019.
If selling to consumers (a distributor in EU speak, but this covers selling through a shop or gallery or craft fair or online or anything else), or manufacturing products for sale (a producer), you need to comply with the WEEE legislation.
There is no minimum level below which you are exempt, so you need to go through the process even if you only produce or sell one lamp a year.

Producers

There is no minimum level below which you are exempt, so you need to go through the process even if you only produce one lamp a year. However so long as you produce less than 5 tonnes of lamps a year you will count as a "very small producer", so the requirements are kept very low.
As a producer, you need to register in your own country. If not in the EU, but selling into the EU, you probably need to register in the EU through a company representing you in the EU, and similarly if selling in the UK but not being based in the UK - this would normally be your importer, if you have one.
Once registered as a producer, you can use the WEEE symbol on your products (the crossed out wheelie bin). You also need to make periodic reports on the weight of WEEE products sold.

Distributors

As a distributor, you need to register in each country that you sell in (whether you are based in the EU or not) - there is no common EU-wide scheme.

UK

In the UK, as a very small producer you can register directly with the Environment Agency, which will deal with registering with the English, Welsh, Scottish or N. Ireland bodies as appropriate: https://npwd.environment-agency.gov.uk. The cost of this is about £30/year.
See here for information on UK producer WEEE requirements: https://www.gov.uk/guidance/electrical-and-electronic-equipment-eee-producer-responsibility
As a distributor, the easiest option is to join the Distributor Takeback Scheme (https://dts.valpak.co.uk), which you can do if you only sell online, or if you sell under £100,000 of electrical and electronic items a year. The cost of this is £74/year.
See here for information on UK distributor WEEE requirements: https://www.gov.uk/electricalwaste-producer-supplier-responsibilities
UK Office for Product Safety and Standards WEEE Page
WEEE guidance: https://www.gov.uk/guidance/regulations-waste-electrical-and-electronic-equipment

EU

As a producer based in the EU, I believe you only need to register in your own country.
However you need to register as a distributor in every country that you sell in to.
Guide to complying with the WEEE directive in the EU, including links to each country's implementation: https://europa.eu/youreurope/business/product-requirements/recycling-waste-management/weee-responsibilities/
Overview on WEEE in the EU: https://environment.ec.europa.eu/topics/waste-and-recycling/waste-electrical-and-electronic-equipment-weee_en
WEEE Responsibilities: https://europa.eu/youreurope/business/product-requirements/recycling-waste-management/weee-responsibilities/index_en.htm
EU FAQ on WEEE: https://ec.europa.eu/environment/pdf/waste/weee/faq.pdf