Next silly question....

If you can bear to do it, there are ready made sauces - at least there are in Germany. I used to bring sachets over to my mother as she loved a hollandaise sauce on her salmon or other fish, and the powdered version was much less fatty than making it from scratch with huge amounts of butter.

Of course, if you are trying to avoid butter completely for any reason (lactose intolerance, strict veganism), you would need to check the ingredients which appear to include butter in some form. But it's definitely not as greasy and fatty as home-made.

The sachets are only available from German import firms, apparently, and the examples I have found seem to be in the US.

germandelistore.com/german-food/cooking/sauces-gravy-mixes-broth/712/knorr-feinschmecker-lemon-butter-sauce

www.germanshop24.com/groceries/cooking/broths-and-sauce-mixes/knorr-feinschmecker-lemon-butter-sauce/

I am back to report total failure.

Now off to follow the sage example offered by corner. It will cost far less than the multiple ingredient range needed to test my way to a questionable outcome!

You will probably get a sauce, but I doubt it would taste the same. Personally, I can’t stand the “margerine” taste in anything, and in hollandaise there isn’t much to disguise it either.

Then internet says coconut milk or almond milk - wouldn’t have a clue if it works. There seems to be a few recipes out there.

Suspect I’d be heading for my nearest ‘posh’ supermarket or delicatessen and hoping. Then I’m just lazy .

I plan to experiment...but thought I would first check the voices of experience, first. No point in reinventing the wheel.

In theory I think it should work. Hollandaise is just whipped egg yolks cooked out by a hot fat.....so hot fat substitute may well work.
Flavour could be the issue.
Fennel...the sauce you describe is essentially a hollandaise, so if the fat and eggs combined cold, I have a mind to think they should combine hot.

Off to fire up the food processor!

Why not try it and see? Try veg. marg. or sunflower oil?
I never use butter in cooking . I make a white or cheese sauce with a roux of veg. marg. and flour, but then add milk. But that's not the same as hollandaise.
I've also made an uncooked sauce with egg yolks melted marg. mustard and some lemon juice and chopped parsley etc. Good with fish or veg.

Cannot see it working personally.

Try looking on a Vegan website, they may give you alternatives.......good luck (let us know how you get on)

No. I don't think it would work as butter is the main ingredient of hollandaise.