There are two issues:
First, the efficiency of a particular reaction is entirely a function of nuclear reaction kinetics, so, you hit the temperature and pressure necessary to overcome the activation energy and you're good to go, regardless of whether that takes you a few nanoseconds or a few million years. It took a long time to get there in the sun because gravity is weak, and gravitational collapse takes a long time. But, once you get there, you're there. With lasers doing the inertial confinement you can get to temperature and pressure much faster.
If you think of it as nuclear chemistry, how you reach the threshold thermodynamic variables will not affect what values the state variables need to have to have enough free energy to push the reaction.
Second, far less importantly, AFAIK, nobody is going to try to recreate the P-P chain that goes on in the sun. It would be nice if we could, but the reason it proceeds so slowly is that the reaction kinetics for P-P fusion basically suck: it requires a weak interaction to stabilize the P-P fused nucleus. Most of the time the diproton (2He nucleus) is unstable and dissociates. An improbably weak decay flips a proton into a neutron in a very small number of cases. (I can't remember the number, but it's miniscule. This is why the sun is burning so "slowly.") The flipped neutron changes the diproton into deuterium, which is stable.
Most fusion researchers have been trying to do fusion with various combinations of deuterium, tritium, 3He, or even 3Li. These lead to more stable nuclei result products, with much more favorable reaction kinetics. Unfortunately, they also produce fast neutrons, which the P-P chain doesn't. As a result, there are radioactive byproducts our sun doesn't produce (in its primary reaction.)
So, to do fusion at achievable energies with decent Q's, we can't rely on the process used in the sun, anyway.
We're comparing steady state conditions over some period of time. The tens of millions of years I cited represents the length of time that the sun could shine on its energy of gravitational contraction, and I'm counting this total energy as the ( non-nuclear) ignition energy. So it takes that long for the sun to "break even" with radiation presumed to originate from fusion. So that's its break even confinement time.
With inertial confinement, the laser blast inputs a certain energy, and the confinement must be long enough so that the fusion reaction generates an equal amount of energy.
Well ... I guess this makes for a difficult comparison, since the laser energy input ( presumed instantaneous ) is arbitrary, whereas the sun's gravitational self-energy is a function of its mass and radius. It follows that my inference that the P-T conditions must "greatly" exceed the solar center had no basis. So I was RRRRRR .... RRRRRR ...., well, you know.