My dog is obsessed with my newborn!

My 3.5 year old dog Lily is obsessed (in a good way) with our 1 month old newborn! When my daughter Everly cries for any reason (changing her diaper, hungry, changing clothes etc) Lily rushes to her side and completely forgets all her training. If I try to breastfeed Everly on the bed or the couch Lily is licking her face, legs anywhere to make sure she is okay until she stops crying. I know this is incredibly sweet but has anyone else dealt with this? How do I re-train Lily when it only happens in the moment and I need to tend to my daughter? Here is our attempt to post a picture of Everly turning one month but of course, Lily had to check on her 😜