If I were mixing lasers to generate a white light source for an old film projector, is there a limit to the colors that can be projected off the film? Sometimes in digital cinema projectors, lasers are used to generate the light and colors, ideally 3 seperate RGB lasers. The range of colors they are capable of creating is limited by the specific wavelengths of each of those lasers, such as what is inside the triangle they would create on the CIE 1931 color space diagram. (If I understand correctly.)

By BenRG and cmglee - CIE1931xy blank.svg, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=32158329
If I were mixing lasers to generate a white light source for an old film projector, and the film had colors that fell outside the triangle, depending on what wavelengths I used, would they still display properly?
 A: The colors won't display properly because of using lasers at all, regardless of the wavelengths of the lasers that were used.
Unfortunately, your goal is misplaced.  You shouldn't use lasers to generate a white light source for old film projection - the film wasn't designed for light sources like that.  Old film requires a full spectrum similar to sunlight in order to replicate colors.  Historically, Xenon arc lamps were used for this, but also Halogen lamps.
If you don't have all the wavelengths in between your RGB lasers, and don't have the power in those wavelengths in the rough proportions of sunlight, the color will not be reproduced correctly.  Hence, lasers won't work regardless of their wavelength - their spectrum isn't wide enough to cover all the wavelengths of sunlight.
Another way to think of it: old film used a spectrum of roughly sunlight wavelengths during its exposure, so you need a spectrum similar to sunlight to shine through it to get the same color.
If you must use lasers, then you must find phosphors that the lasers can excite, which re-emit the light with a broader spectrum.  Then mix the phosphors until you get a spectrum similar to the lamps above.
Side note: Digital projectors work under different assumptions about the 'film' they are projecting - there is no physical thing that light must shine through to produce the image.  The digital projector is effectively decoding instructions, equivalent to 'make this specific color appear on this specific digital image pixel'.  In that scheme, you need to know the color space used to encode the digital data, and then the lasers must combine such that 'pure' red matches the red vertex of the color space.
