The phrase "lavish attention" means to give a lot of care, time, and affection, usually going above and beyond what is expected or necessary. Full definition
Make sure you don't lavish attention on the new arrival. (dogsbarn.com)
A trio of bigger clubs that all the pundits fall over themselves to lavish attention over. (chiesaditotti.com)
Every four years, presidential candidates lavish attention (and, more important, campaign promises) on a dozen or so swing states whose electoral votes are up for grabs. (nymag.com)