Many astronaut autograph collectors prefer NASA lithographs to have signed. If you collect these 'lithos' because they're NASA-issue, or have captions on the back, that's fine.
However, if you prefer color lithos because they will last longer than photos, you might want to rethink your reasoning...
The Lithographic Process
Lithographs are produced from a printing press. Art is scanned with a camera and filters (analog) or on a high-end drum scanner (digital) and broken down into four constituent colors: cyan, magenta, yellow and black (CMYK). Negatives are produced in each of these colors, and then each is further reduced into individual dots, usually 133 to 150 per inch.
Next, sheet-metal printing plates, with a photochemical coating, are "burned" like a photographic print from the negatives. These are then wrapped around cylinders on a printing press, imprinted with one color at a time, until the image is reconstructed.
The Death of a Lithograph: Acid Deterioration and Fading
As an artist and gallery owner, I've personally overseen the production of hundreds of lithos, both art prints and promotional flyers and catalogs. For the fine art prints we use an acid-free paper, special light-resistant inks, and a non-yellowing varnish.
Highly acidic paper (newsprint is an extreme example) yellows and browns and becomes brittle over time. As such, NASA's specs at the U.S. Government Printing Office call for their lithographs to be produced on acid-free paper, and my tests show that some indeed are. Some, presumably older lithos, are not.
No one at NASA seems to know, but my guess is that at some point the space agency became aware of the need for longer lasting documents, particularly books and reports. This may not have been the case in the early days of the space program, when acid-free stock was rare and expensive.
The NASA printing office also told me they use a varnish on NASA lithos "which in time will yellow." A varnish is a clear coating that helps prevent fingerprints.
Then there is fading. Depending on how much ultraviolet light the litho is exposed to, the vegetable-based inks used in lithography can be severely damaged.
Fluorescent lights are the worst, giving out large amounts of color-sapping ultraviolet light.
You might think direct sunlight would be bad (and it is) but surprisingly, reflected sunlight is almost as bad. That's because reflected sunlight, for example from a north-facing window (in the N. hemisphere) is primarily blue. The shorter blue and ultraviolet wavelengths bounce around more readily then longer, redder wavelengths.
Usually, the red (magenta) inks fade first, leaving a bluish cast to the litho. Flesh tones and moonscapes grow colder. The difference is subtle at first, and you may not even notice unless a full-color version is seen alongside.
Photographs
You are most likely familiar with the analog photographic process. Now there is a digital process which can take a file (JPEG, TIFF, etc.) and output sizes up to 10x15" prints on regular photographic paper.
Kodak prints -- magic words for many years, and exclusively used by NASA -- are not the best. Far from it. Kodak rested on its laurels and market share for far too many years, and were overtaken in quality and price in the late '80s. Significant advances in photographic sharpness, color saturation and longevity have emerged during the last decade. Gone are the days when your family color photos would quickly yellow and fade away (even if carefully stored within albums).
Today, most photographic paper is resin-coated (RC), a polyester coating surrounding the emulsion. Polyester remains supple much longer than any paper, and as it is almost impervious to humidity, acid deterioration is much less a concern.
Photographs are also "continuous tone" rather than divided into four colors of tiny dots as in lithography. As such, subtle color blends and details are superior on photographic prints.
As for fading, results vary based on the different types of photographic paper.
The best is Cibachrome by Ilford. Cibachromes are used for archiving color photos by museums. They are entirely polyester based, with non-fading metallic-based color dyes (as opposed to vegetable based). They are made from positives (transparencies or slides) rather than negatives. I used to test market limited edition art prints first on Cibachrome.
The problems with "Cibas" are that the colors are extremely saturated (I liked that, but some photographers don't), they have a subtle metallic sheen, they are a bit contrast-y (again, personal preferences), and the "paper" is sensitive to heat, tends to buckle, and resists mounting. They're also very expensive.
Next is Fuji Crystal Archive paper. This is what most modern photo labs use, because it is less expensive, and offers superior color, detail, and longevity.
As mentioned earlier, Kodak paper, despite its reputation, is one of the worst for longevity. Witness older NASA photos, which are always yellowed, curled, and lacking in warm flesh tones.
Different testing labs use different measures of light and fading, but Kodak paper consistently appears to last for 75% shorter than Fuji Crystal Archive. One reliable lab lists unprotected Fuji as lasting 80 years in bright light before any measurable fading occurs. No measurable fading occurred in the dark.
Both lithos and photos can be stored in albums in the dark, or they can be displayed, but if the latter is chosen than not in direct sunlight or near unfiltered fluorescent light. Framing should be done archivally, with conservation glass or UV plexiglas -- both block 98% of harmful UV rays -- with only acid-free materials (mats, backing) touching the item.
If stored in the dark, inert, acid free materials should also be used, in controlled humidity (no more than 40%) and in cool temperatures. They should also be kept out of range of noxious or reactive gases, such as car exhaust. Bags of silica gel can help with humidity.
Pick the image, not the material
In conclusion then, lithographs are no better than photographs for longevity. Lithos are more fragile, more susceptible to moisture and have inferior color and sharpness.
Furthermore, more NASA images are available as photos, especially in black and white, which is almost completely stable when compared to the relative fragility of color.