Yes April is Luke biological daughter. Basically Luke and April's mum Anna were dating for a while years ago, and then i think when they broke up and Luke went to live in Stars Hollow, she probably found that she was pregnant, but decided not to tell Luke about this.
The three guys that April took hair samples from were her mother's old flings, and Luke was amongst them.

your dumd he had a thing with this lady and she got pregant the lady didnt know who was the father so 13 years later april ased her who her dad so the lady gaved her 3 names of who could it be and she took luke dna and mached it with hers and luke didnt know he had a kid so no she was not adopted

She is his biological daughter.

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April is Luke's biological daughter. he didn't forget about her. he never knew she existed. when him and anna(aprils mom) broke up anna hadnt told him she was pregnant. i dont know how she got the 3 guys.

Luke is arpril's real father and he dindt know he had one cause arpils mum never told luke.

April is Lukes REAL daughter Luke didnt know that April was born he had no idea about her and there were three possible fathers because her mom probably dated these guys so April had DNA tests and she found out Luke was the one who had her DNA