Mendez dived to head home on the hour and Lee stooped to clinch the points when he headed home seven minutes from time.
Grimsby had little to offer in retaliation, although keeper Kevin Pilkington made a vital save in each half to maintain County's lead.
After a physical first half Notts played more football after the break and they had pace throughout the side which was too much for an at times pedestrian Grimsby outfit to counter.
Mendez scored a goal which was something he did not manage while at Grimsby last season and Lee's clincher merely rubbed salt in some very sore wounds.
There were six old boys on show - four former Grimsby players in the Notts line-up and skipper Paul Bolland and defender Nick Fenton facing Notts.
For Notts it was a welcome return to form after their hiccup at home to Bristol Rovers last week with manager Steve Thompson reverting to the tried and tested line-up which kicked off the season.
They rarely looked like conceding, were competitive in midfield and had pace and guile up front to trouble a shaky Grimsby back-four.
Both goals came from crosses with the first brilliantly executed by midfielder David Pipe and were scored in front of a healthy away following from Nottingham.
For Grimsby they just cannot seem to generate any rhythm, although being without three first choice strikers is clearly not helping.
With the players who left the club in the summer to go on to better things there is still a sense of disappointment after the play-off failure and realistically the best they can hope for is to finish in mid-table.
For Notts, who basically have a new line-up this season, the future looks bright and if they maintain this form a challenge for automatic promotion is clearly on the cards.