Writing on his fundraising page, Parrish said mountain rescue team volunteers searched tirelessly for Luke and were available ”365 days a year to respond to emergencies in the mountains and remote areas of Scotland”.
Thousands of pounds have been raised on the charity page, with many tributes made to the runner.
Parrish was a member of the Dumfries Running Club, where he was club champion in 2022.
He began running in his late teens before building up to racing in his early 20s, taking part in a series of local 5km and 10km races.
Parrish later joined the marines and previously spoke of using running as a way of decompressing from the demands of the job.