burning lambs

The neighbours might get suspicious that you are Pagans because you have a barbeque?

And this isn't a troll?

Okay I'll take your word for it. My neighbours generally don't get suspicious that I'm a Pagan despite my always wearing a pentagram around my neck so I don't think you've much worries there.

They're more likely to think you're a Muslim, given that lamb features a lot in Middle Eastern and North African cusine.

A bigger concern with the neightbours would be either:

1. The smoke blows towards clothes they have drying on the line, leaving their wash smelling of cooked lamb.
2. They feel put out that you had a barbeque and didn't invite them.

The first is a serious concern, and I would advise that you forewarn your neighbours of your barbeque for that reason.

To answer the more sensible question:

what do pagans eat anyway? is there a strict diet?

There are no dietary laws of Paganism as a whole. However some traditions may have some dietary rules (though I can't think of any right now).
Vegetarianism is probably more common amongst Pagans than in the general population, but isn't universal. This is partly related to their Paganism, all Pagans have a respect for nature, and in some cases that leads individual Pagans to decide not to eat meat. But also related to the fact that those people who practice Paganism today are often people who will question our culture's practices, and so wouldn't just eat meat because they'd never thought of doing otherwise.
While it isn't a dietary law as such, some may feel that they would not be acting as good Pagans if they ate meat. For example a Wiccan that considered eating meat (whether all meat, or just meat obtained by modern farming practices) to be harmful would be going against the Rede if they ate it, whereas another Wiccan who honestly saw nothing wrong with eating meat would not be prohibited from doing so. (For the record I eat a lot of meat myself).

There are dietary traditions, which is a slightly different thing to dietary laws. Generally Sabbat feasts would heavily feature seasonal foods, the strongest such association being the consumption of bread and other baked goods (Mmmm… donuts!) at Lughnasadh, which is partly a celebration of the grain harvest. Those who do eat meat are likely to eat a good deal of it on the winter Sabbats of Samhain and Yule.

Once upon a time, before importation, preservation and hot-housing allowed us to eat anything at any time of the year, this would simply be a matter of eating what was available to eat at the time.

While there aren't dietary laws as such, food features heavily in Pagan culture. Food is one of the most obvious ways in which we are dependant upon nature for one thing. Pagans belive in enjoying the physical plane, rather than focusing solely on the spiritual side of things, and food is an imporant part of that.
Gifts of food are a big part of the culture and if someone allows their home to be used as the venue for a sabbat, esbat, or just an informal get-to-gether then they may often find themselves struggling to find somewhere to put all of the food that the guests bring with them.

There are also some folk traditions (e.g. colcannon at Samhain), modern borrowing from mainstream culture (e.g. turkey or goose at Yule) and revising of old religious traditions (e.g. pork at Yule, reflecting an old Egyptian relgious custom), but these are more to do with a respect for tradition that often goes hand-in-hand with Paganism than with Paganism per se. I normally eat pork at Yule (wild boar for preference, hey it's a holiday so I might as well splash out) but I wouldn't feel I'd done anything wrong if I didn't.

Ritual use of food is another matter. The stereotype in some quaters is of animal sacrifice, which I assume is what your question was based on. This does happen but:

1. It is extremely rare.
2. Is most commonly practiced within Candoble, Voodoun, Yoruba or similar paths of which it is very debatable whether they could really be considered part of "Paganism", or at least part of the same Paganism as is Wiccan and Druidry.
3. The animals are generally slaughtered humanely, arguably more humanely than in modern abattoirs.

On the very rare occasions that someone does practice, or even discusses the theory of animal sacrifice, this it tends to be very controversial within the Pagan community (unsurprising given the high number of vegetarians that community includes).
The only extent that most Paganism does contain animal sacrifice is that many Pagans who eat meat would give more thought to the animal that died so that we could have the meat than others might. As such we can no more be said practice animal sacrifice than any other meat-eater, but are more aware of it.

Use of herbs is much more common. This includes medicinal herbalism, but also ritual use and also being aware of the symbolism of the herbs one uses in cooking. For example not only would a rosemary go well with your lamb (mint is over-rated for lamb IMHO but this isn't a cooking board so I won't go into it) but it is also symbolic of rememberance (as Shakespeare of course has Ophelia state) both in the sense of remembering those who have passed and also memory skills (rosemary oil is good to use when studying), and hence I might decide to eat rosemary with that in mind (also it's yummy).

Witchcraft, and some other traditions, have a very strong use of food at rites. This is called "Cakes and Ale" or "Cakes and Wine" but any food and drink can be used (for one thing if you have a drinking problem then using wine would be very unwise, if you have coeliac disease then cakes containing gluten would also be out). It is arguably the most important part of any rite in witchcraft (other paths have similar practices, but I can't speak as knowledgably of them).
The cakes and ale starts with a blessing of the drink, and then the food (in some traditions only the drink) with an athamé. The athamé is a ritual knife, often with a black or dark handle. It is generally blunt, since it is never used for cutting (some traditions have an exception that athamés can be used to cut wedding cake) and hence the only thing sharpening it would do is increase to risk of an accident, or of one being accused of carrying an offensive weapon when bringing it somewhere.
That said there are some traditions that don't believe in have "special" tools and they would have a sharp athamé because then it's better for peeling potatoes
The blessing of the chalice of wine with the knife is a sexual symbol, and hence a symbol of the process of reproduction that is required for us to have food and everything else that nature provides us. If the practitioners are to have a feast or dinner-party as well as the rite then they would generally have some or all of it then, as opposed to the meal being a separate thing to the rite.
Because the cakes and ale are considered so important I would generally try to have some form of it in an impromptu rite (because I suddenly felt like one, or to work for someone who suddenly fell sick etc.) even if all I could muster was water and some bread and jam.

Yes, we'd have the sense to have a big bonfire to keep us warm as well.