It would be hard to argue whether Shakespeare intends the play to be all in all a love story, a lust fest and a lust for power.I personally think, as an ardent reader of Shakespeare that there are all elements of the three notions that you mentioned above in the play.But above all I think the tittle "Antony and Cleopatra" speaks for itself.It is indeed a love story and a tragic one.
Cleopatra's first designs was to use Antony for her national needs in the first place using lust and seductions which remains an integral part of the play throughout.We also learn that Cleopatra was previously married to Caesar and also had relations with Pompey.She is hedonistic; she gives herself fully to the power of love, she heeds no other consideration but for her own immediate desires.Both of the characters of Antony and Cleopatra are full of lust – for life, for power, for each other.
Cleopatra understood that her path to greatness lay chiefly in her ability to influence world leaders, as she had influenced Caesar. Rome then was the world super-power, and Cleopatra had no desire to be indebted to Rome as her father Auletes had been. The only hope of restoring Ptolemaic greatness would be to side with one of the Romans against the other. Cleopatra's seduction of the three men -Pompey, Ceasar and Antony inorder to be in Rome's favour and the great battle fateful battle which eventually follows all depicts that this play is also a struggle for power.Hope this helps.:)