I do believe that if it ain’t broke, don’t fix it. If Liz Earle works for you, is in your budget, and you like the products, that’s great and there’s no reason you should feel you have to change. I like some of the Liz Earle products. I have super dry skin, tends towards dehydration, and have always been prone to patches of eczema.
There’s some evidence (mixed quality) on omega-3 fatty acid supplements improving atopic conditions including eczema, though variation in genetic predisposition and environmental factors play key roles in atopic responses too. Stress often triggers flares too, but I’m sure you already know that!
If you fancy a change from Liz Earle, Eucerin do some great facial creams and their plain day cream in a tube is incredible as a daily staple for me. But the ingredient urea does not suit everyone with eczema, so it might not work for you - it’ll depend on the type and nature of your eczema.
Avene has a great range of products for sensitised and reactive skin, they have an emulsion that reduces redness as well as restores skin barrier. La Roche Posay is lovely, one of my favourite brands, but a lot of their products are quite heavily fragranced and not everyone likes that. I don’t use their fragranced products, but LRP’s Toleriane range is nice and gentle as well as being unfragranced - I use the lotion cleanser every night and it does a terrific job.
Sunblock is useful to help manage the impact of solar damage on delicate eczema-prone skin - LRP’s daily SPF50+ is the absolute best IMO, no white cast, and has the best chemical filters on the market. Other sunblocks are available of course! Oh and Aveeno Skin Relief with Shea butter - usually used for body skin - is good at arresting a face/neck flare-up IME. And “cica creams” (active ingredient centella asiatica) can help manage flares too, again I love La Roche Posay’s one (cicaplast) but most parapharmacie brands offer something with centella these days.