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There are more photos, surely?

Pl either post these or supply the PCN and VRM and we can look ourselves.

In any event, IMO the degree of incursion is greater than would be accepted by an adjudicator as 'de minimis'(legal term AKA too trifling to worry about) so your mother's* only plea is for discretion. However, an adjudicator may not exercise discretion and therefore this would have to be targeted at the council.

The reason I've leapt ahead to adjudication is because discretion cannot be considered and therefore absent prospective procedural errors on the council's part, which wouldn't become evident until the statutory discount has lapsed, the discount should be kept in mind. You should know that a 'section 25 crossing', which this is, does not require a traffic order and therefore this - often fruitful- line of enquiry is closed off. If this council re-offers the discounted sum even after unsuccessful formal reps then the matter could be taken to this stage at least - the stage where most procedural improprieties manifest themselves.

'Could have moved forward', then why didn't she? Did this space only arise while she was parked, if so, for how long was she parked?

*- is you mother the registered keeper with current DVLA details?

IMO, that photo doesn't suggest there was room to move forward - and unless you were there then you don't have first-hand knowledge.

In any event, as regards the contravention IMO the argument goes to mitigation only.

Pl post the back of the PCN where most of the procedural parts have to appear.

Your link supposedly to the back of the PCN only shows the front of it.

We need to see the back, because we don't often see Lincolnshire PCNs so there may be fatal errors in the small print that render it void. The content of a PCN is defined in law.