I read The Folio Society edition of this book several years ago and found it to be less a biography of Cleopatra than a Marxist social history of the conflict between, on the one hand, the Patrician Class of the late Roman Republic and its empire as represented by such figures as Brutus, Octavian, Cicero and Cato the Younger (although in the latter case, I may be conflating my memories of this book with those of the entertaining HBO series, "Rome"), and on the other, the conquered Eastern provinces of the Empire, the lower classes of those provinces and Rome itself, and their representatives, Caesar, Mark Antony and Cleopatra. At that level, Lindsay's book is fascinating, especially in its description of the plebeian yearning throughout ancient history for a pre-historical "Golden Age" of freedom and plenty absent class-domination and oppression. Lindsay also offers a welcome corrective to the traditional view of Brutus as "the noblest Roman of them all," noting, if memory serves, that he was the biggest moneylender in the Empire, and that his agents in Cyprus, for example, charged interest at the rate of 40% or higher.
As for Cleopatra herself, Lindsay covers her leadership of the East in rebellion against Rome and her alliances with Caesar and Antony well, but I never got much of a sense of her as a personality. Lindsay's Cleopatra is a diplomat, a political and war leader, and she and Antony, in particular, are popular spiritual and temporal figures, but she is not a full-blooded person. For that, I imagine there are far better books, but for a discussion of the international implications of class conflict, ancient Apollonian "liberation theology" (Antony and Jesus as variations on an Apollo as Liberator) and colonial unrest in the Roman civil wars, Lindsay has a lot to offer.