Did Lactantius ever say why it was good for Christians to be ruled by a Christian emperor? Lactantius was a Christian who had been a part of the Roman government (which was hostile to Christians) prior to his conversion. Sometime between 303 and 311 he wrote a systematic theology, in which he wrote:


  When [God] might have bestowed upon His people both riches and kingdoms, as He had before given them to the Jews, whose successors and posterity we are; on this account He would have them [that is, "His people"] live under the power and government of others, lest, being corrupted by the happiness of prosperity, they should glide into luxury and despise the precepts of God; as those ancestors of ours, who, ofttimes enervated by these earthly and frail goods, departed from discipline and burst the bonds of the law.


But when Constantine converted to Christianity and became emperor, Lactantius became an advisor and hagiographer to Constantine, as well as a tutor to the emperor's son. It appears that he believed it good and right for a Christian to hold the highest post in the government, even though he had previously said that it was for Christians to live under a pagan emperor.

Did he ever say why it was good for Christians to live under a Christian government?
Edward Gibbon tells us, in The Decline and Fall of the Roman Empire, (D.M. Low abridgement page 290), as soon as the defeat of Licinius had invested Constantine with total dominion of the Roman world, he immediately, by circular letters, exhorted all his subjects to imitate, without delay, the example of their sovereign, and to embrace the divine truth of Christianity. Lactantius was very possibly being pragmatic taking on the role of eulogist for an emperor who gave favours to those who became Christians. 

Anders Cullhed says, in The Shadow of Creusa: Negotiating Fictionality in Late Antique Latin Literature (ebook) Lactantius saw an opportunity for covert, albeit legitimate Christian indoctrination. Cullhed says Lactantius considered it downright legitimate to treat truth as a contraband of sorts, concealing it by means of a lie. The siginificance of this is that we can never know whether Lactantius sincerely believed anything he said in support of any position he took. He knew that Constantine looked favourably on work that progressed the Christian cause in his empire and did not need any reason to do the emperor's bidding and would naturally say it was good for Christians to live under a Christian government.