The Lecale Way currently has a set of ways east from Downpatrick to Strangford, and a relation “Lecale Way (Ulster Way Section)” from Strangford south to Newcastle. However, in Strangford, things get a bit complicated.
Here’s what’s in the east-west bit, and here’s what’s in the north-south bit - there’s a bit of overlap.
Which bit belongs where probably depends on the Ulster Way route here. The connecting piece seems to be part of this, so presumably this relation should connect to the ferry - but does the Ulster Way go round the coast or straight along the A25?
I have noticed this confusion myself.
I think it going to be difficult to figure out a definitive answer - there are a few somewhere-between-public-sector-and-quano-ish sites such as https://walkni.com/ which purport to have ‘definitive’ mapping of Northern Ireland’s walking routes, but I fear they often contain errors, and then the actual signage on the ground (which in this instance is probably the responsibility of Newry, Mourne & Down District Council) is not always well maintained and may be contradictory.
It’s further complicated a bit because several of the better bits of the Ulster Way are co-signed as medium-distance trails (such as the Lecale Way, Mourne Way, Ring of Gullion Way, Newry Canal Way etc etc) - which seems to have been tagged on OSM using some nested relations which can get their knickers in a twist when there’s extra bits of the medium-distance trail which aren’t part of the Ulster Way too.
And a further issue is that route of the Ulster Way was ‘revised’ a few years ago and basically about a third of it was scrapped. But to save face, sites like Walk NI talk about ‘link sections’ which are ‘on road with no pavement’ and ‘best traversed using public transport’ (despite there usually not being any…) . Ho hum.
Anyways, according to Long Distance Walk - WalkNI the official Ulster Way bit goes round the coast, not along the A25 (Ordnance Survey maps contradict this, saying the Ulster Way goes along the A2…)
Whereas the Lecale Way goes in that extra loop along the A25 https://sp-orni.s3.eu-west-1.amazonaws.com/trails/default/walk/Lecale-Way-Section-1.pdf
If you don’t mind peeking on Google Street View, you can see the current fingerpost singage at the crucial junction here Google Maps which contradicts the Walk NI map and OSNI map 
That signage is then further contradicted by the microscopic signage at this junction Google Maps
All in all, I think what you see today on Waymarked Trails - Hiking is probably the least wrongest option. (Although I would prefer to see the pavement on the A25 drawn as a separate way and the walking routes tagged along that, rather than along the carriageway of the road!)