Synonyms for Gaga (same or very similar meaning)
WordNet sense 1 (mentally or physically infirm with age):
doddering, senile, doddery
WordNet sense 2 ((used especially of persons) having lived for a relatively long time or attained a specific age):
old
WordNet sense 3 (marked by foolish or unreasoning fondness):
crazy, dotty, enamored, infatuated, smitten, in love
WordNet sense 4 (feeling or showing love and affection):
loving
From the ODE community, based on WordNet
add/edit