Oh, a little baby bottle fed lamb. Exciting.
I advocate for good quality goats milk. It's the closest mammal milk to sheep that most people have access to. I haven't had any scours yet, nor have I met a farmer who bottle fed a lamb goats milk have any trouble. I think it's more technique of feeding than the milk itself. But then again, we've only done with raw goats milk... so perhaps the pasteurization and homogenization does something to the milk that the lamb has trouble digesting.
Other people have other opinions. A lot of it will depend on what you have access to.
I haven't raised a bottle bummer this early in the year, so it's a bit too cold here for a lamb to be outside 24 hours without a warm body (like mummy) to keep it warm. I can't really say what you 'should' do, but I'll tell you what's worked for me in the past.
We set up a run outside the front door. A variation on the run we use for mummy and baby ducks. Inside the run, there is a dog crate (small at first, bigger when the lamb grows) with
hay in it for bedding (and a feed bag under the hay for easy cleaning). During the day, the lamb is in the run, or beside us while we work in the garden, and do other chores. During the night, we bring the crate inside - but BEFORE we turn the heat on / start the fire for the evening. Too sudden a change in temperature can be really hard on any animal, little lambs especially. If I'm spinning, on the computer, or watching a film, I keep the lamb on my lap. Otherwise it's in the crate near us.
Sheep are very social and they need a flock to belong to.
I halter train the lamb as soon as it's big enough to wear a halter, so that it can come with me in the car and
swindle cute people out of free animal food like brewery grain and leftovers from the grocery store. Lamb doesn't come in the shop with me, but being outside the shop while another member of the family goes in shopping, usually gets people's attention.
The halter helps when the sheep is too big for the run, we can tether it near something that needs munching on.
You'll probably get lots of (conflicting) advice, and not all of it will work for you. Use the resources you already have and follow the method that matches your values.
One other thing to think about is vaccination.
Do you want to vaccinate? Most farmers do and most vets recommend it. Since the lamb is not on yummy mummy it isn't getting the antibodies from her, so it's something to consider.