Surely if that was their desire then surely they would bother building this new station as the gradient even for light rail would be significantly gentler from Horsforth. Unless the aspiration was to build somethin akin to a cliffe railway.
The vertical distance from Google Map's contours between Horsforth and LBA seems to be about 75m (see terrain view). A light rail link can handle much steeper gradients than a conventional rail link, and also doesn't get in to the weeds of what services etc.
To keep the gradient reasonable any mainline station is likely to need to be reasonably deep underground - not impossible to construct, but rather expensive and also then extends journey times for passengers with large amounts of luggage to get up to the airport terminal itself.
For comparison:
Heathrow - 83m passengers a year - Dedicated branches for dedicated express, EL and LU, 2x coach links to other stations
Gatwick - 40m passengers a year - direct mainline station, advertised express (although not exclusively airport now, I think).
Manchester - 30m passengers a year - dedicated branch on mainline, dedicated tram service.
Stansted - 30m passengers a year - dedicated branch on mainline, dedicated express link.
Luton - 16m passengers a year - dedicated parkway station + shuttle to terminal, advertised airport link.
Edinburgh - 14m passengers a year - dedicated tram link, mainline parkway nearby.
Birmingham - 13m passengers a year - mainline interchange, dedicated shuttle
Bristol - 10m passengers a year - Shuttle Bus link to Bristol Temple Meads.
Glasgow - 7m a year - Bus link to Paisley Gilmour Street
Belfast International - 6.7m passengers a year - Bus link to Belfast Grand Central. Station proposed on Lisburn-Antrim line if that reopens.
Newcastle - 5m passengers a year - T&W Metro dedicated link
Liverpool - 4m passengers a year - links to Liverpool South Parkway nearly 3 miles away
Leeds-Bradford - 4m passengers a year - bus connections to local stations and Leeds/Bradford city centres.
This would suggest that a dedicated mainline branch isn't really justified for Leeds-Bradford, but that a localised shuttle or extension of a future tram link probably would.