Luckily, not the case.
Most lactose intolerant people switch to soy milk, which has most of the same properties as cows milk, and also comes in different flavours, like cows milk.
Us lucky few who can not have soy milk either, still have options though.
1) Sanitarium So Good Rice Milk
I didn't particularly like this, it was just a bit too watery and flavourless. Although it was the first one I tried, it could have been me not liking it because it was such a change.
2) Vitasoy Rice Milk
I preferred this one, it has a fuller, smoother taste, and the consistency was more like regular milk.
3) Vitasoy Rice Milk Vitamin and Mineral Enriched
I was happy using this one, it is very similar to the Vitasoy Rice Milk Original.
4) Vitasoy Rice Milk Protein Enriched
I wasn't so keen on this one. It's protein enriched by adding chickpeas to the mix. It's more yellow in colour, and required vigorous shaking to break up those slimy little lumps you can sometimes get. The flavour was also not quite to my liking.
5) Liddells Lactose Free Cows Milk (Low Fat)
This is milk by an Australian company, I've only been able to find the Low Fat milk here in New Zealand, but on their website they have a range of milks and also cream! I would be very excited to get my hand on some of that. It is sweeter than regular cows milk because the lactose in it has been converted to galactose and glucose. I guess an easy way of describing it is us lactose intolerants can't digest and convert the lactose into these chemicals, so it has been already pre-digested.
Because of the conversion it is sweeter than regular cows milk, but it seems to still have all the same properties as regular cows milk, and so I've found it is the best substitute in baking and cooking where milk is called for.
I haven't been able to find this yet, if anyone knows where to get it in NZ, do tell me!
Edit: So I found Oatmilk (in Masterton of all places). It's also made by the Vitasoy company. It took a little while to get used to, but it's the closest in consistency to regular milk. It isn't as sweet as the rice milk, or the lactose free milk, and when having it by itself I found it had a slight odd after taste. I hear that it is a good dairy substitute in baking, although I didn't try.
7) Coconut milk/cream
There are a lot of recipes out there that are twists on usual favourites, but use coconut milk or cream instead of cows milk. You can also get it in powder form - Maggi Coconut Milk Powder Mix. You can make both coconut milk and cream from this, but it does have milk protein in it so is useless for people allergic to that. It has a fantastic rice pudding recipe on the back, which is great because I was always a fan of that delicious dessert.
I've read that you can make whipped cream by putting a can of coconut milk in the fridge for a couple of hours or over night, then opening it, separating the watery part and the thicker creamy part, and whipping the creamy part in a cold bowl with cold beaters. You can add a bit of icing sugar to sweeten it if needed, I'm yet to try this but I'm keen to. You can use the leftover watery part in smoothies or something.
A lot of these substitutes are sweeter than regular milk, so if I use them in sweet baking I like to cut down on the sugar a bit.
The main thing when changing your milk is to shop around and try different products to see which you prefer.