The note reads: "According to the Cert[ifica]te of the Rev[eren]d G. Morland transmitted to me 30th August."
An Act for the better regulating and preserving Parish and other Registers of Births, Baptisms, Marriages, and Burials in England (Stat. 52 Geo. 3, c. 146) describes the reason why this was written in the margin:
IV. And be it further enacted, that whenever the ceremony of baptism
or burial shall be performed in any other place than the parish church
or churchyard of any parish, (or the chapel or chapel-yard of any
chapelry providing its own distinct registers,) and such ceremony
shall be performed by any minister not being the rector, vicar,
minister, or curate of such parish or chapelry, the minister who shall
perform such ceremony of baptism or burial shall, on the same or on
the next day, transmit to the rector, vicar, or other minister of such
parish or chapelry, or his curate, a certificate of such baptism or
burial in the form contained in the schedule (D) to this act annexed,
and the rector, vicar, minister, or curate of such parish or chapelry
shall thereupon enter such baptism or burial according to such
certificate in the book kept persuant to this act for such purpose;
and shall add to such entry the following words, 'According to the
Certificate of the Reverend __ transmitted to me on the __ day of __.'
Therefore, the baptism did not take place in the church on 30 Aug, but was performed elsewhere. Perhaps the child was sickly and not expected to survive, so was baptised at home. Often this is recorded in the register as a private baptism. The child would not have been re-baptised in December, but the second entry may correspond to the time when the child was received into the church congregation, which concludes the rite of baptism.
The certificate sent to the rector would have been of the form:
It would be a long shot to check whether the certificate has survived. If it has survived, it would likely be archived at the local register office within the parish chest material. In this case, you can scan through the Lancashire Archives catalogue for Lancaster Priory material, found in piece PR 3262. Some of this material has been filmed by FamilySearch and digitised, and can be viewed for free online with a FamilySearch account: see Parish records in St. Mary's Church in Lancaster, 1707-1900. As I say, it is unlikely that you will find the certificate, but it is worth checking. You never know what scraps of paper the curate of the day thought were worth keeping.