Wow, this menu is very similar to what I served last night, which was also BYOB. I agree with Champagne for all of it. Here's what we had, all of which would probably work with your menu:
First: Roederer Estate Anderson Valley Brut Rosé, Agrapart et Fils Les 7 Crus, 2007 Herve Azo Petit Chablis. Those would be great with your Jerusalem Artichokes, I think.
I'm not sure about the beets and carrots, mainly because I don't like them. But Whiner's rec. of an Austrian Riesling sounds good.
Here's where your menu and mine overlap: I did a roasted sea bass, which I served with roasted cauliflower, and a butterflied leg of lamb with an herb crust with roasted red potatoes. For the fish, someone brought a 2002 La Chabisienne Premier Cru Récolte, and 2004 Meursault Chapelle et Filles. Both white Burgundies, the Chablis being lighter without oak, and the Meursault fuller, with significant oak. I preferred the Chablis, but that's my palate more than anything else. People also continued with the Champagne and Petit Chablis during this course.
For the lamb, a New Zealand Bordeaux blend, 2000 Te Motu. It's 74% Cabernet Sauvignon and 26% Merlot. It's a classically styled wine, and provided a classic pairing. The other wine brought for this, a Gigondas, didn't get opened, as, by this time, we were happy and full! But, like Whiner says, Southern Rhone is a very good thing with lamb. I did mine in a very Provençal manner, with rosemary, orange zest, and garlic, which is harmonious with Rhones.
I also enjoyed the Meursault with the lamb. I think its richness stood up to it quite nicely. Although it was gone by the time we served it, I think the Rosé would have also been good with it. I'm saying this because of the strong fruit of the sparkler, and the bubbles provide a nice counterpart to the richness of the meat.
Well... Champagne actually goes with all of that, but I would be particularly keen on pairing it with the Jerusalem artichokes.
Beets and carrots (roasted?) I'd go Austrian white. Preferably Riesling.
Cod I'd go Italian white... Probably either a medium-bodied Friulian or else from Trentino Alto Adige. Maybe a Gewurztraminer from the Alto Adige for my first choice. (A dry Gewurz from Alsace or one of the few good ones from the US would also be nice.)
I don't know what Raja's lamb is, but based upon the sides and how most lamb dishes are, I'll cautiously reccomend a southern Rhone.