One of the few things we know about Luther’s pilgrimage to Rome is that he didn’t meet the Pope. There’s no reason that he would have even tried. His business was an internal matter within the Order of Augustinian Hermits, and religious orders had their own separate chain of command. It would likely have taken a much larger matter to get the Pope’s attention at that time.
For Pope Julius II was off at war. Now before this elicits a flurry of protest, or embarrassment, or any other typical 21st-century response, it’s important to remember that in 1510 the papacy, and the church for that matter, was a very different thing than it is today, politically speaking. In addition to being spiritual authorities, the church and the papacy in particular were major landholders. As such, they wielded a tremendous amount of temporal or what we call political power.
It’s all a bit confusing to sort out “spiritual” vs. “temporal” authorities within the medieval church. Up to half the land in many places belonged to various monasteries, parishes, bishoprics, etc. And wherever the church controlled the land, the king got little or even no tax money. In late 1510 Julius II was away dealing with what were clearly temporal matters, fighting alongside the Venetians to keep the Italian province of Romagna out of French hands.
Julius, the “Warrior Pope,” was known for his skill as a diplomat and a fighter but not really as a spiritual leader. This was common in those days, and while the papacy maintained it symbolic role as the head of Christendom in the West, there were many who criticized the wealth and politicking of the church while remaining in good stead within it (Dante, for instance, was one of them). The religious orders, including Luther’s Augustinians, would not necessarily have expected strong faith or consistency from the Pope in the way we would. To them he was as much king or emperor as he was pope. He was one power among many that had to be dealt with for them to go about their business.
That the papacy is as “spiritual” (as opposed to temporal) as it is today is a testimony to how different today’s church is from that of Luther’s day. In fact, internal reforms over the last 500 years have made today’s Roman Catholic church look more like that envisioned by sixteenth century reformers than could ever have been imagined by Luther, who never met in person the “Warring Pope” or any of his successors.