Here is the beginning of the Friberg entry for the word:
[Fri] eivdw/ VSRA--1S oi=da
oi=da the perfect of the obsolete ei;dw (see) used as the present;
Thayer's entry begins this way:
eivdw/, i;dw, Latin video (Sanskrit vid, perfect veda know, vind-a-mi find, (cf. Vedas); Curtius, sec. 282), an obsolete form of the present tense, the place of which is supplied by o`ra,w. The tenses coming from eivdw/ and retained by usage form two families, of which one signifies to see, the other to know.
So it would appear that BYM is perfectly correct in using the lemma underlying the form oi=da, even though this lemma never appears as such in the New Testament.
The next time BW updates the Greek alias file, the Thayer entry for eivdw/ will be able to display with the other entries for oi=da.