Let me tell you why it probably doesn't.
Lactose is a milk sugar. It is broken down in the small intestine by an enzyme called Lactase.
Lactose intolerance is caused by a lack of lactase enzyme which is usually attached to the lining on the wall of the intestine.
If the lactose sugar is not broken down and absorbed in the small intestine then it will carry on travelling down the gut undigested.
When the lactose sugar reaches the large intestine (the colon) the bacteria and other microorganisms there think that it is Christmas. Usually they feed on scraps of left over undigested food and, all of a sudden, they have lots of sugar! There are a lot of bacteria and they breakdown and ferment the sugar as quickly as they can.
If you have ever brewed your own beer, wine or cider, you know what happens when microorganisms get hold of a lot if sugar! Yeasts breakdown sugar to ethanol and carbon dioxide; bacteria breakdown sugar to lactic acid and carbon dioxide.
As the gut organisms break down the sugars, acids and gases are produced. The gas causes bloating and wind (my kids would call this farting) and the acids and other broken down sugar products pull lots of water through the bowel wall into the poo. The poo is then big, watery and irritating and it is rapidly expelled from the body as frothy explosive diarrhoea which may burn the skin around the bottom. Lactose intolerance poo is Bristol stool chart 7.
If you understand this mechanism, you can see that Lactose Intolerance cannot cause vomiting or eczema or rashes or anaphylaxis. It shouldn't occur with other foods unless they contain Lactose.
So how do you get a lack of LactAse enzyme?
Some babies are born without LactAse - this is called Congenital Lactase Deficiency. It is a very rare genetic illness mostly seen in those of Northern Scandinavian, Latvian or Russian ethnic origins. I have never seen this in the UK, so the chances of YOUR baby having a Congenital Lactase Deficiency are virtually zero. (Remember I am a UK Paediatrician writing for a UK audience!).
Some people lose their LactAse enzyme as they get older. This is called Primary Lactase Deficiency and it is very common in some ethnic groups. LactAse is lost in virtually all Asians and Native Americans and over half of those with Hispanic or Black origins. However, again thinking about the UK, it occurs in only 2% of Northern Europeans.
Primary Lactase Deficiency rarely presents before the age of 2 or 3 years so it is not the cause of milk problems for babies in the UK.
So, if it's not Congenital or Primary Lactase deficiency, could a UK baby have Secondary LactAse Deficiency?
Secondary LactAse Deficiency is caused by damage to the wall of the intestine. The lactase enzyme is on the end of little fingers on the wall called villi and so are easily damaged.
So what can cause this?
Coeliac disease can damage the intestine villi and cause a Secondary LactAse Deficiency. If your baby is having the symptoms of Lactose Intolerance and the problems began at the time of introducing wheat or Gluten (Wheat, barley, malt, oats, spelt) then consider Coeliac disease, especially if you have a family history of this.