The only "original" record i have been able to locate to date of Lysbet is her second marriage, below from Flatbush DRC Marriage Records 1677-1757:
1679 14 Dec; Wouter Gysbrechtsz, ym of Hilversum, Holland; Lysbeth Jans, of Gouda wid Frans Bloodgood, liv Flushing
Flatbush DRC Marriage Records 1677-1757
She is quite clearly at this time using her own birth surname (Jans) just as would be expected of a good Dutch woman in the era, if she was not using the name Bloetgoet/Bloodgood at this point in her life there would be little to suggest she took it up later in life.