Hi there
I took my son to the hospital at one point when he was about 3 months old because he had a D&V bug that was really bad. One of the things we were told by the paediatrician was that when infants get a tummy bug, it does lower their levels enzymes and cause their body to lose the ability to break down the lactose in milk, and it can continue for three to four weeks. This isn't a temporary "milk intolerance" as milk intolerance is an inability to digest the milk proteins, which is very different from lactose intolerance, which is the inability to break down the milk sugar. So yes, it is normal, and very common.
My own personal thought would be to NOT switch to a lactose free formula, for a couple of reasons -- first, a baby's digestive system is very sensitive to change and a change in formula can be hard on their system. It also usually causes changes in bowel movements for a couple of days, and so you wouldn't know if that was the change in formula, any further illness, a reaction to the formula, etc. Secondly, because your LO isn't lactose intolerant, her body is just using the enzymes elsewhere to do different jobs while it's healing from being ill, and thus having a bit of trouble with the lactose at the moment, which is different than being lactose intolerant. Keeping her on her regular milk will help her build back her strength and her body regain the ability to break down the lactose. It may sort of seem like her bug is lingering a bit, but that helps her build the strength up and to fight it should it come again.
HTH?