Can electrons change the frequency of light as they bounce off/around? I know that light does not interact with other light, but can interfere it, at least its amplitude. With that said, lights frequency can be changed via bouncing off matter, where matter might absorb some of that photons energy changing the frequency.. Does this imply that a high energy beam of light that intersects an non-visible beam of light, might be enough to bounce the light around at the intersection of the two laser beams to emit visible light? By changing its frequency? Could that also be controlled by the energy output of the other laser?
 A: There are two ways to look at light/electromagnetic_radiation.
a) classically
In this case two light beams can interfere depending on the phases and their frequency.

For optical beat frequencies below 10 Hz the interference of the
  light beams is observed on a viewing screen as a slowly drifting Michelson interference fringe pauern.
  For beat frequencies greater than 10 Hz the drift ofthe interference fringes is too rapid to be observed
  visually; however, if a photodetector is placed so as to detect light from within the rapidly drifting fringe
  pattern, the time variation of the detected light signal can be amplified and fed to a loudspeaker, allowing
  an individual student or a lecture audience to hear the beating of the two light beams

When one starts talking of electrons, one is talking of particles and there we go to the
b) quantum mechanical framework.
In this framework the light beam is composed of particles called photons,with energy E=h*nu  (nu is the frequency of the EM wave), which when scattering off an electron  may  change frequency in the process, transferring energy to the electron or taking energy from the electron. For lower frequency photons, Raman scattering also changes the frequency of the impinging beam with a small probability:

When photons are scattered from an atom or molecule, most photons are elastically scattered (Rayleigh scattering), such that the scattered photons have the same kinetic energy (frequency) and wavelength as the incident photons. However, a small fraction of the scattered photons (approximately 1 in 10 million) is scattered by an excitation, with the scattered photons having a frequency different from, and usually lower than, that of the incident photons.4

In the quantum mechanical framework a photon could scatter off a photon through higher order QFT diagrams but with extremely small probability for visible light both because of the many vertexes which go down 1/137 each and the off mass shell of the exchanged particles in the diagrams. It can be studied in particle accelerators. 
A: Going by your title, yes, electrons can interact with light to shift its frequency. See the link, posted by @experimentX, to Compton scattering . Going by what you have stated in your actual question, two lasers interaction would be a higher order processes. For example something like electron-positron pair creation via photon-photon interaction (Note that one of the lasers would have to be very high energy for this to occur). The $e^+/e^-$ can then annihilate to give you photons again. However, I am guessing you are not thinking of the latter situation.
