Firstly, as a short description or label, it's quite ok not to use a full sentence, but the key is to ensure the reader can easily understand what's written.
To that end, the decision here involves not only syntax (word order), but also voice (passive or active) and tense (the choice between simple past "ran", and past participle "run") [although that might be simplifying it too much].
If it's meant as a statement of fact, you have two ways of abbreviating the full sentence:
- "Your scan was last run on Tuesday" [passive voice] becomes "last scan run [date]", or
- "You last ran this scan on Tuesday" [active voice] becomes "last ran scan [date]"
The key component here is probably the time/date element: it helps to establish context, whether it's part of the expression itself, or clearly relates to the timing (e.g. it's the heading for a date column, or it's text that appears next to a date field).
On the other hand, if it's meant as a description of the scan itself, then "last-run" (note the hyphen) functions as an adjective describing the scan:
- "This is your last-run scan" becomes "last-run scan".
A good example of the complexity of our language in three short words!