Why would a frame lack serial numbers?
Even if you find the serial number, its absolutely no use in identifying the bike without a brand/manufacturer.  There is no global index like auto VINs.


Serial numbers are used for several different purposes.


Identifying a frame through production, for logistical and tracking reasons
Identifying a completed bicycle through a sales process
Uniquely identifying a bike for warranty purposes
Identifying a bike for insurance purposes.


At no point is a bicycle frame serial number used to identify the bike's model or age or manufacturer.    A frame's serial number is not related to a car's Vehicle Identification Number (or VIN.)

For a frame to lack a serial number could be any or


The frame was hand made by a small-run frame builder, or home made.   Most frame builders would use a serial number of some format though, even though their monthly output could be single digits.
The frame has been repaired and the serial number was lost by replacement.
The frame has been stolen and resold, with the serial number ground off or filled-and-painted-over.
The frame was legitimately repainted and the serial number is obscured or hidden (my bike's like this - the S/N is visible but illegible.
The serial number is covered by an accessory (very unlikely)


But most likely, you simply haven't found the serial number.  Common places for serial numbers:


Under the bottom bracket
On top of the bottom bracket housing
Up the side/front/rear of the  seat tube
Up the side/front/rear of the  down tube
Up the side/front/rear of the  head tube
Inside/outside the chainstays
Inside/outside the seatstays
Inside/outside the rear dropouts.


Less common areas to find a serial number


INSIDE the bottom bracket housing
Down inside the seat tube.


Places you won't find the serial numbner


On any mechanical part - they may have their own serial number, but it won't be a frame serial number
On the fork - again it may have a fork S/N or replicate the frame's SN or it may not have a serial at all
Inside any closed tube - the headtube, BB and seat tube are the only tubes in the frame with some level of visibility, so it won't be anywhere else.