All of mine are purple flowered and podded, so I have no first-hand knowledge but:

Qince Dolichos is basically the same genetically as the garden peas that Mendel used, I would imagine the same relationship of dominance. The color should dominate over the white. That said, the implication of intermediate colors would argue for lack of a dominant/recessive relationship and more for an additive relationship as in mirabilis, but I doubt this. If there are other colors, it is probably a seperate gene mechanism at work.

There other species of dolichos besides lablab.

George

I don't know specifically about lablab beans, but in many other plants the purple/lavendar/blue shades involve a pigment and a co-pigment, often chelated with a metal ion. This applies to chicory, hyacinths, bluebells, balloon flowers, etc.

White is the lack of pigment. Red/pink results from the loss of the co-pigment.

White should be true-breeding if protected from cross-pollination. The others might segregate, so you'll need to test each plant separately to see what might be lurking within.

To test your purples you should raise 24 self-seedlings from each plant. If a plant produces all 24 purple-flowered offspring there is only one chance in 1000 that the parent is homozygous for purple/white.

Mendel raised only 10 offspring per plant, which means he would have misidentified 5 or 6 "hybrid" plants as true-breeding.

Karl

Dolichos lablab is most closely related to Vigna and Phaseolus and then Glycine (soybean) so they might be the best to examine for genetic relationships.

Typically the 'wild-type' is dominant and mutants are recessive (but not always).

Purple then would be expected to be dominant and white to be recessive. However, dominance/recessive relationships depend completely on how the phenotype (appearance) is measured and categorized.

As an example, a cross of a purple with a white might produce coloured offspring. If we classify the purples as coloured and the whites as not coloured then coloured is dominant. But if we classify the purple parent by the wavelength of light it reflects, and so on then the 'colour' (wavelength) of the offspring might be intermediate between the two parents and the inheritance is co-dominant or additive, and so on.

In soybean (Glycine) purple is dominant over white. There is a pink that is recessive to purple in soybean.

In Phaseolus much work has been done on seedcoat colour but some work has been done on flower colour. Again purple flower colour is dominant to pink which is dominant to white in a series of alleles. However, in this case there are two genes involved P and V. P (purple) is dominant to p which is nearly white. In PP or Pp individuals V controls the colour such that V/- is purple, a particular V allele labelled lae creates pink flowers and v/v has white flowers.
Bichemically, the coloured pigments would be anthocyanins and in white or near-whites the pigments would be flavonoids and related compounds from earlier in the biosynthetic pathway.