What does he mean when Clara tells him to change the future and he says "I could have once, if the time lords were still around."?
He is implying a new set of regenerations (which he ultimately gets anyways). Clara is asking him if he can change his future, which means The Doctor NOT dying on Trenzalore. That could be possible only if he could've received an extra set of regenerations, which only the TimeLords could grant him. So That is what he meant by that sentence.
Time Lords, as suggested by "Father's Day" and "Rise of the Cybermen", used to be "overseers" of sorts when it came to time and space. They kept interactions between parallel worlds in checked and prevented any paradoxes from getting out of hand. If they were still around, the Doctor would have been able to change the future with little consequence because they could have intervened in order to contain the paradox. Luckily, however, they were still able to help him change the future in some way, but it took some convincing by Clara in order to get them to take action.
It was my understanding that the Time Lords had apparatus that went above and beyond the capabilities of Tardis(es?) to affect the universe and multiverse.
Recall that when Ten and company was marooned in the parallel universe, he stated that once, before the fall of the Time Lords, travel to and from alternate universes and across the Void was possible, but now, without them, he was at the mercy of physics and his own intellect.
They had means that we do not see, and which are separate from their physiology, so then it must be a device or technology. Something that could modify the timestream without creating a paradox or that would fix or null paradoxes that did occur somehow.
The set limit of a regeneration cycle is something that the TimeLords could manipulate. I believe it was first seen in "The Five Doctors" when different incarnations of The Doctor were taken into the Death Zone on Gallifrey, in which The Time Lords had The Master help them by offering him a new regeneration cycle. In fact in the current episode "The Time of the Doctor" you see the Seal of the High Council, which The Master was given to prove his good intentions in which The Doctor took from him.
Since The Doctor was on his final life, the only way to change his fate was to have The Timelords themselves give him new regenerations, and since they were trapped in another universe he could not ask them for help, because he knew that if he answered the question that would lead to a new Time War.