There's not really any standard for what "better" or "not better' color is. There are only more saturated or less saturated colors, and colors with a cast or tint in one direction or another around the color wheel. What one considers "better" or not is strictly an individual opinion.
There are standards for capturing and displaying accurate color, but that does not seem at all related to the example images in the link included in the question.
Some lenses do have a slightly "warmer" or "cooler" look to them.
Lenses can render different color tints based in varying transmittance of the different wavelengths of light. No lens passes 100% of the light that strikes the front element all the way through to the image plane on the other end. Different materials used to make various lens elements vary with regard to their transmittance of different wavelengths. Improvements in lens coatings that reduce reflections (reflected light is "lost" light) have increased the ability of modern lens designers to create more color neutral lenses. Most lens designs in the digital era attempt to be as color neutral (and thus maintain maximum transmittance) as possible since color is almost infinitely adjustable in post processing when using the raw data from a digital sensor.
In the film era this color adjusting flexibility after the fact was not so much the case and lenses were made and sometimes marketed as "warmer" or "cooler" based on whether they allowed slightly more of the red/orange/yellow light at one end of the visible spectrum or more of the blue/indigo/violet at the other end to pass through the lens to the film that has more rigid color response characteristics. We couldn't alter the ISO or color response curves on every shot from a single roll of film with the push of a few buttons. It took a LOT more work (i.e. time and money) in the darkroom to fine tune color, contrast, etc. than we can now do with raw digital data. Those very slight differences in transmission and color are now trivial to adjust after the image has been taken.
As they age, some older lenses may even induce other tints, particularly if they contain radioactive elements with short decay, such as thorium that yellows as it ages.
Other lens characteristics that affect our perception of "color" in images.
One thing that many say will help the colors in an image to "pop" is often called micro-contrast. It is a description of how well a lens renders contrast between edges in the scene. Much has been written about micro-contrast. Here's one example. Here's another. Some of it is even mostly correct, such as this example.
One of the "mystical" ideas circulating around certain circles about micro-contrast is that a lens with fewer elements will have better micro-contrast than a lens with more elements. Those who make and market lenses based on very early lens designs, such as the Lomography lens you reference, like to emphasize the "purity" of the low number of lens elements and how it makes images created with the lens "three dimensional" and have an "illusion of depth."
While there is a lot of hookum out there concerning "micro-contrast", it is the case that a lens that can render more tonal values (levels of brightness) smoothly can also render more pleasing transitions between brighter and darker areas with the same color.
How the "color" of a lens looks is also related to the overall contrast it can render. Veiling flare, for example, destroys both overall contrast and slight differences in colors. Lenses with high numbers of elements tend to be more susceptible to flare under certain conditions because they have more glass/air interfaces than lenses with fewer elements do. Flare is caused by reflections at glass/air interfaces, as well as by scattering of light that can be caused by things such as heavy dust on optical surfaces. Flare will be most evident under conditions in which strong backlight is in the scene or strong light sources just outside the angle of view of the lens are shining into the lens at an angle.
What makes the images in the kickstarter ad distinct?
It's mostly the way they are post-processed. There's a lot of color stuff going on. Some of them look like they've been processed to simulate the idiosyncrises of different types of color film. Others are just highly processed using tools, such as HSL (Hue-Saturation-Luminance) - a/k/a HSV (V=Value) or HSB (B=Brightness) - that allow adjusting the hue, saturation, and brightness of different colors independently.
Related questions here at Photography SE:
What image-quality characteristics make a lens good or bad?
What is "micro contrast" and how is it different from regular contrast?
Does opening the aperture improve color contrast? (Open aperture producing more punchy colors / closed aperture more dull colors?)
Why would one lens produce warmer colors than another?
is there a real difference between "digital" and "film" lenses?
Why does image quality vary across lenses, and what to look for when comparing?
What is the advantage of a lens with a curved focal plane? (Older lens designs generally leave field curvature uncorrected or less corrected than newer "flat field' lenses made for things like "macro" work, do.)