Hi MacFee.
Vegetables - on Low Carb High Fat (LCHF) you don't need to have plain boiled or steamed vegetables. Have a Google for flavoured butters. They are simple to make, you can often keep them in the freezer in a long butter sausage in greaseproof paper and just slice a chunk off when you want some.
Kerrygold does a garlic and herb butter and Lurpak does a garlic butter if you're in a rush.
This is a pretty simple recipe for steamed veggie with garlic butter sauce made fresh. You may find that cooked carrots spike your blood glucose, you might not.
http://blog.weangreen.com/steamed-vegetables-with-garlic-butter-sauce/
Bearnaise sauce and Hollandaise doesn't use flour but if you don't cook much, you can buy them in jars.
It's been said that boiling new potatoes, cooling and storing in the fridge, then making into potato salad with mayo and chives makes them lower carb, but you'd need to test blood glucose. Some people find raw carrots spike them, some don't.
If you aren't using high sugar store-bought dressings, then pretty much any vinegar other than balsamic can be used in a dressing. You just mix oil (olive, avocado, sunflower, rapeseed/canola) with vinegar or even lemon or lime juice. Bung in mustard or herbs or salt and pepper, make sure that you taste it and that it's thoroughly mixed. Or you can buy mayo, IMO Hellmann's is the best and you want the full fat stuff. There's no rule that says you can't plonk mayo or dressing on your plain veggies either - really good with green beans.
Google is your friend, you can look for recipes like creamed mushrooms or have a rummage in the tinned aisles and find tinned vegetables such as ratatouille, fried onions and Indian and Mexican things, If there's a shop catering for Eastern European, Chinese or Indians - any cuisine really you could have a look for new things there.
Posh cook books in the library are likely to have flourless but interesting veg recipes with cream and butter, which you could photocopy or there's the vegetarian/vegan thread on here. Things like lentils, spelt, quinoa might or might not spike you.
Rose Elliot wrote a book called The Low Carb Vegetarian, which you might be able to get hold of.
So basically butters, butter sauces, Bearnaise, Hollandaise, dressings, mayo, foreign veggies and vegetarian recipes.