I've enjoyed these sauces on vegetables:
In Amá, Josef Centeno has a Vegan Cashew Queso that may be good if a cheese sauce was a favorite. I found a modified version of his recipe here on NYT Cooking. I see many others online.
That book also has a delicious Cilantro-Pecan Pesto that he serves with roasted cauliflower. The recipe is available online here.
The "Torrada" sauce that he serves on roasted broccolini is also delicious. Made with pecans, walnuts, garlic, anchovy, cilantro, olive oil, lime and various seasonings. He describes it as a Mexican-inspired version of the classic bagna cauda, which might also be a possibility.
Along the lines of the Tahini & Miso dressing that @BeeZee mentioned, Mollie Katzen has a recipe for a Miso-Almond Sauce to be served on steamed vegetables, tofu and/or noodles. I used to make that over and over. Here's an online version. You can make it with any nut butter and any sort of miso. Three ingredients. No cooking.
The Pine Nut Vinaigrette from Six Seasons appears online here. You can sub other nuts for the pine nuts.
The same book has a Caper-Raisin Vinaigrette that is also excellent on vegetables. The recipe uses a 2 ounce tin of anchovies, which I think make it delicious but this online version omits them for a vegetarian version. You choose.
Those 2 above are somewhat tangy so they may not suit someone who doesn't care for your lemon/olive oil mix. I think the other flavors balance that out, but everyone's different.
In the creamy but non-dairy category, Shaya has a preserved lemon aioli that he serves with crab cakes. I think it's great on steamed vegetables...or on a spoon! I can't find it online but can paraphrase it for you if you think it would be of interest.
Editing to add this link to the fabulously flavorful tonnato that Mandy Lee of Lady & Pups calls, "Tuna Sando Sauce." It's amazingly delicious!
