Lugsden made 56 appearances between 2018-20 during his first spell at the Harry Williams Riverside Stadium.
Meanwhile, 24-year-old McKenna began his career in the Bolton Wanderers youth ranks before joining Witton Albion as an 18-year-old.
A short spell with Runcorn Linnets followed before a return to Witton, where he made 41 appearances last season.
At the beginning of this season he joined City of Liverpool, featuring 10 times in total.
The Rams are currently bottom of the Pitching In NPL West Division, having picked up just three wins from their opening 15 league games.
The two new recruits both started in Saturday’s goalless draw at home to Colne.
It was the first time they had kept a clean sheet since the middle of August.
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