Hi Xia Here closely could considered like carefully, or even better intimately.

Logically, it would have to have the second meaning, simply because it isn't possible to kiss someone without being in close proximity to them. However, I don't think that any native English speaker would say this - it doesn't sound right to me. You can kiss someone hard, passionately or deeply, for example, but I have never heard of 'kiss closely'. Where did you find this sentence?