i think this should absolutely be balanced according to the sunlight straight sword, if the S3 is a support faith straight sword, then this should be a solo/invader faith straight sword
current stats for me with 30/35/30/40 at +5:
S3: 196+207(403) with S3 buff: 449
LHS: 196+159(355) with S3 buff: 396
so one might say "well just make the scaling the same and give a pontiff-like buff to the lhs right?" NO, see, that's not enough because while it might seem that the oath of sunlight is just a buff for the S3 and as a support for your friends AND your other weapons(which i guess could be balanced saying that the LHS W-art is just sas strong if given a pontiff buff extra skill) it also adds on top of it the fact that the S3 can be buffed both by magic and items, while the LHS can't in ay way other with body boffs like oath of sunlight and sacred oath.
given that from will never make the LHS buffable, i'd say give it the same str/dex scaling as the S3 but with even better faith scaling aswell as the pontiff like buff.
consider that the S3 along with a crystal chime+5 lightning blade and the oath of sunlight with those stats(which should be less or more the ideal for these straight swords, at least by intuition without considerin int) gets to an absurd 617AR, a non-buffed dark lothric sword is 548(c-c-a-a), while a lightning one is 498(d-c-s)
in my opinion, it should have enouh faith scaling that with those stats it should reach by base stats the AR of the S3 with S3 buff and with the pontifflike buff it should reach about less or more the strenght of the lightning lohric sword with these stats(which should be stronger with say, 30-40-35 than the buffed lhs with 30-35-40)
so in short:
give the same physical scaling as S3
give it abundantly higher faith scaling than S3
give it a pontifflike W-art buff
and also change a bit the scaling of the lightning lothric sword to match a slightly more physical damage focused build than the self-buffed LHS, so that it wouldn't be too weak in comparison.