There may be scope for containers from Liverpool to the north-east, but north-west to north-east is probably too short for rail to be competitive.
Once Peel extends the railhead at Seaforth for which they already have planning permission, then the economies of scale will start to kick in and reduce the cost making east/west movements by rail more cost-effective allowing shipping lines which control the majority of movements of individual containers to concentrate their road transport on the final mile delivery to the customer.
At some point next year Freightliner is expected to become part of the second-largest global shipping line CMA CGM, whilst the largest shipping line MSC already owns the UK's largest road haulier Maritime Transport Limited through it's wholly owned subsidiary Medlog, who I believe already operate a terminal at Doncaster. MSC, it's wholly owned subsidiary WEC Lines and CMA CGM all operate sailings in and out of the Port of Liverpool.
Intermodal Logistics Park North (ILPN) which is the trading name of the new freight terminal at Newton Le Willows was purchased over two years ago in an off market deal by the developer Tritax presumably because they had a customer interested in operating the site.
Whilst it's known that Freightliner have taken "an interest" in the site, it's not certain they were the party behind the purchase of site as the scheme also includes some substantial capabilities which would be more akin to the sort of operation conducted by Maritime Transport Limited, plus the fact Tritax were also behind a similar scheme at Hinckley for Maritime Transport Ltd.
The actual owner of ILPN remains a mystery as the company has been registered in the Channel Islands so it's not possible to discover the ultimate owners through UK Government records, but the site will largely be used to handle intermodal trains from UK southern ports and is unlikely to have services to and from the Port of Liverpool.