So the father is unknown.
There is a certificate stating that the father is unknown. But there is something to tell! The lastname Tighelaar suggests that the unknown father has this lastname too. The firstnames Pieter Ynzes suggests that the father has the firstname Ynze (Ynzes with the s at the end, meaning “son of Ynze”). Wich results in the name of the father: Ynze Tigchelaar. Often firstnames were passed on to there children, so Pieter might be the firstname of the father. And so we end up with the name of the father: Ynze Pieters Tigchelaar
This Ynze has trully lived in the timeframe Lijsbert lived. And also around the place Lijsbert lived. And so a connection is there between Lijsbert en Ynze but without being married. And from this relation, Pieter Ynzes Tigchelaar was born, being the forefather of this family Tichelaar this family tree is all about.
These are all assumptions, without any evidence but very likely. One problem is that the names mentioned above were quit common. The names were spelled differently: Cuperus was also known as Kuperus or Kuipers. The name Ynze was also spelled as Yntse or Ynse.
Another thing is that the lastname Tigchelaar was adapted in 1811 by law of Napoleon, Ynze being 20 years of age, there is a certifiate for this. It is not clear (yet) if the lastname was used before that time. Probably yes, because the profession was related to the name Tigchelaar.
Below the addition to the family tree wich was not added.