At low temperatures, the activation energy for pure CH4 O2 oxidization is about 170kj/mole. (See figure 1 here) That’s about 1.8eV per atomic reaction.
1.8eV can be provided by 688nm red light, or any shorter wavelength. So generally, visible light can initiate reactions.
I can’t quantify how many photons/cm2 it’ll take to start a runaway reaction from the liberated energy, but LMethane/LOX is an ideal mix for turning a few catalyzed interactions into runaway combustion: unlike air, it has no N2 to carry away energy or slow the kinetics. Mixed liquid reactants increase the rate of CH4 2O2 configurations. Etc.
(more detail added:)
Typically, a combustion reaction starts when heat is added, which provides activation energy to enough molecules for some to react. The energy (really, enthalpy) from those reactions provide the activation energy for the next, which provides energy for the next, etc. Once started, only more reactants is required if each time there's a surplus of energy after losses.
That question of "after losses" is significant. If you're burning with air instead of pure oxygen, some of the heat goes into heating (and perhaps disassociating) N2. Some gets conveyed away through the thin gas reactants, so remaining reactants don't get enough of the energy. Etc. Those are all losses. Ideally, you have pure (so other chemicals can't take heat or drive other reactions) fully mixed (so any molecule that picks up energy can react) liquid (ditto) reactants; those are easiest to ignite and will burn fastest.
A fully mixed LCH4 LO2 environment is about as good as you can get for those conditions. Once some activation energy is provided, the resulting reaction energy goes straight to nearby reactants that are ready to use it. It’s so favorable that the mixture actually detonates, with the combustion front moving as a shock wave at about 4600 m/sec.
The only countervailing term I can think of (I haven't done any experiments with this stuff!) for optical ignition is the long optical length of light in LCH4 and LOX: The incident light isn't absorbed right away, so spreads its energy along a path. (That can be useful if you want to ignite the while volume all at once, though)