I have been watching this topic from a distance. Bottom line is that the oral history doesn't seem to match the recorded data. But then, also the recorded data may not always be the truth. Hence my small contribution to try to fact-check and verify the recorded data, or at least determine the plausibility.
First, the person of Lambertus Ooms. There is no question about when and where he was born (1871, Schijndel, the Netherlands), who his parents were, and when and how he came to Indonesia (with SS Soembing from Rotterdam, september 14th 1895 to Batavia/Jakarta, october 22nd 1895). Also, since he was 'afgegaan' (left military service) in 1907 in Ngawi I think it is at least plausible that the person buried under the headstone marked 'L. Ooms' in Ngawi is in fact this Lambertus. There appears to be nothing to contradict this, and recorded facts do support this conclusion.
Second, the person of Darsinah (Ooms). Her last name Ooms is recorded nowhere in the official data, but comes from oral history. The official data we have comes primarily from the marriage certificate (1921) and the passport application (around 1950). Now we stumble upon a discrepancy:
(19 Nov. 1921, thanks to Leo for digging this up at the LDS) "[...] and the native woman Darsinah, born in Meester Cornelis, estimated 34 years old, living in Malang, daughter of the native [man] Arsin, deceased, and the native woman Rakinem, living in Walikoekoen, department Ngawi" Official data, which allows simple mathematics to roughly calculate Darsinah's year of birth to 1921-34 = 1886/1887. (B.t.w. Johannes Dirven's stated age of 35 matches his year of birth 1886)
Now, if/when we believe the estimated age of 34 year to be approximately true, then Lambertus Ooms cannot be her father, since Lambertus must have been 15 or 16 years old, a schoolboy living with his parents in Schijndel, the Netherlands.
However.....,
There is also the passportapplication dated around 1950. And there Darsinah's year and place of birth are recorded as '1897 in Djatinegara' which DOES allow for Lambertus to be her father. 10 years difference. Hmmmm....
Both official documents do state that 'Arsin' is the father of Darsinah. Which fully contradicts the oral history. Now is there any data to further conclude what is the truth? Yes, there is, but unfortunately it doesn't all point in the same direction and is not conclusive at all. First, there is Darsina's passing in 1980: "My mother was born in 1962 and Darsinah died around 1980 (right when my mother was pregnant with her 2nd child)." That makes her age at death about 84 or 94. Both possible, with - of course - 84 more likely compared to 94. And then, there is her photo on the passport application. Which - to me - does look as an Indonesian woman of about 55 years old. But 'looks' can be deceiving.
So when I have to guess, I think Darsinah would have been born in 1897 as the daughter of Arsin and Rakinem. With Lambertus Ooms possibly being her 'stepfather' after Arsin either died or left Rakinem. But that is a guess; no more.