I have been looking into this quite extensively since you raised it and done nothing but draw blanks ... I put the following proposition forward as to what it referers to.Flaybrick
Hill Cemetery was originally opened as Birkenhead Cemetery although it had both names used locally. The original part of the cemetery was about 16 acres and designed by Kemp. In 1890 the quarry was taken over by the cemetery extending it to about 26 acres, this new section does not seem to have been used until the early 1900s. I believe the 1900 reference to Birkenhead Cemetery may just be reference to this new section. Chapel lane may just been an internal reference to paths within the cemetery.
I can find no reference to a Chapel Lane in Birkenhead, though if you have any areas you suspect, I can check it on maps of various dates.
Any other known locations are attached to churches and as such would be called graveyards not cemeteries, yet presumably it has the road named Chapel Lane implying that a chapel must already exist. Alternatively it was built on virgin land, a road AND a chapel were purpose built in which case I am sure we would not have any trouble finding records for it.
There is a slight chance that this has been a mistaken location and there is another Birkenhead Cemetery in some other part of the country/world - I haven't found any likely cases but Birkenhead, Auckland would be the strongest contender with 3 cemeteries dating from at least back to WW1 (I think). The trouble with the internet is one mistake can proliferate quite quickly and become fact so easily.