For the lamb, google roast lamb cooking times and calculate according to the size of the joint you have, I tend to prefer a longer slower cook if you have the option, but so long as you don't overcook it it will be delicious either way (lamb is perfectly safe/nice to eat pink in the middle, like beef). If you have the time/energy (and perhaps this is too late now if its for christmas day), it's nice to make a little marinade of oil, crushed garlic and chopped fresh rosemary (or dried will do if you don't have fresh), rub this over the lamb a few hours before cooking or overnight, and then leave it on to roast. Gravy is tricky with lamb as any juices will likely be fatty, but if you are able to skim off the fat you can make it the same way you would chicken or beef gravy, add stock, seasonings, maybe a slug of red wine to the juices, then something to thicken it (I use a little cornflour made into a paste with cold water) and simmer until tasty...
Parsnips I like roasted in the oven, peel them, chop into batons and (optionally) par boil for 10 mins, then put in a baking tray with some oil, seasoning and a drizzle of honey, then roast in a hot oven (180-200 depending on if your oven is fan or not) for about 30 mins if you've parboiled or perhaps more like 40-45 if not, until a knife slides through the middle easily and they are crisp on the outside. You can simply boil or steam them if you are short on oven space, treat them like carrots basically, but they can be a bit bland for my taste if not crisped up...
Brussels you need to trim off the outer tatty leaves and the woody stem, then (optionally) cut crosses into the tips, then I like to fry them on a medium heat in a bit of oil or butter and some bacon... the key is to not overcook, start checking after 5-10 mins and they shouldn't take longer than 15... add more butter and seasoning to serve!
Good luck!