Carlisle was originally named for the god Lug (Lleu/Llew/Lugh), its name likely meaning "Strength/fortress of Lug" and so one would expect to find strong traces of a cult following at a place named for him. Most assume this would mean huge shrines to Mercury, but this isn't the case. At Luguvalium, Lug was not equated with Mercury, rather he was invoked in his aspect of war-ruler and associated with Mars. This makes sense, given that the town was primarily a military outpost, that the name itself invokes his strength, and is in keeping with his portrayal in Celtic myth in Ireland and Britain. Of Lleu it is said that he was "fortified in the middle of oppression/conflict" and another stanza says he was "A man who invited attack". It is absolutely clear that, despite how this god is presented by some in the neo-pagan community, he was thought of by the early British and Irish as a divine personification of a youthful warrior.
A number of dedications and altars to Mars have been recovered from the area of Carlisle, with some interesting epithets. Chief of interest is Mars Barrex, or Barrecis. This is a title only known at Luguvalium and seems to mean "Mars the Highest/Mars the Supreme One". This seems a fitting title to the Lug presented in Irish myth. Another is Mars Belatucadrus. This title seems to mean "Fair, shining one" which is in fact an apt description of Lug as presented in Irish myth. Belatucadrus was a somewhat popular title used throughout northern Britain, and may also be related to Mars Cocidius. Cocidius seems to mean "The Red One", related still to the modern Welsh word for red, "Coch". In Irish myth, Lug is strongly associated with the colour red. Poetic descriptions of him describe his face like the red rising sun and having red legs. In other sources he is said to represent three colours: Red, Bronze and White. Other figures named Lugaid are also associated with red, such as Lugaid Red Stripes and Lugaid Red-Hand, and seem to be the origin of the Red Hand of Ulster.
Finally there is Mars Ocelus. This is the most interesting of the lot. Ocelus has no agreed upon understanding, but perhaps it is related to the Latin for eye. He is known from another inscription in Caerwent, where the inscription reads "To Mars Lenus, also called Mars Ocelus Vellaunus, and to the spirit of the Emperor" perhaps linking this god to the protection of the sovereign. Vellaunus is known as part of the name of Cassivellaunus, It may be related to the word for victory, or mean chief or leader. Its other known use in relation to a deity comes from Gaul, and is used together with Mercury. Mars Lenus has widespread worship in Gaul and is generally seen as a tribal protector also related to healing. Now one might suggest that all of these iterations of Mars are separate deities. Some of them may be, but it is doubtful that all of them are, as is evidenced by the above example. In fact they are mostly epithets for the same god, manifesting in different functions. Examples from Gaul show that Mars Toutatis was sometimes identified with Mercury as well. Nodens is likewise sometimes associated with Neptune, other times with Mars or even Silvanus. But in a town named for the god, we need to look at the information provided by archaeology. The evidence suggests that Lug was identified with Mars at least at this site. The examples from myth fit with such an interpretation. Let us go through them. 1) Lug is armed with a spear: Not just any spear, the unstoppable spear of death. The main attribute of Roman Mars is his spear.
2) Lug wears a helmet: The helmet is described as being worn to lessen the brightness of his countenance (or conversely causes the brightness) in either event, he is luminous and likened to the sun (but not the sun!) The second identifying attribute of Mars is a helmet.
3) Lug's name glosses as Warrior or Hero: The very name 'Lug' in Old Irish means warrior. in Welsh it is much the same. The Grave Stanza of Myrddyn calls him "Lord of Battle" and his own grave stanza says he "Invited attack" and "Was a fortress amidst oppression"
4) Lug is a protector of the harvest and summoner/slayer of storms: This is perhaps his most critical role in myth. He is strongly connected to agriculture, plants,. trees, milk, fruit and the flowing of waters, unlike Cuchulain who is designated protector of cattle. He regulates weather to bring the right conditions for the harvest, protects the boundaries of the territory and keeps the forces of the underworld in check at those boundaries. This also seems to be the archaic function of Mars in the Roman tradition.
5) Lug is known for leaping: The dedicated priests of Mars would perform special dances to bless fields and promote fertility. They would leap around upon fields and before departing armies to bless them.
6) Lug's spear is said to move on its own accord: A spear of Mars that was said to have fallen from the sky was kept in the god's temple. It was said to shake whenever a war was approaching,
7) Lug is a divine father to kings: Mars is the divine father of Romulus and Remus, the founders of Rome and the first kings of Rome.
8) Lug is associated with the storm: Mars was also in archaic times associated with rain and storm, which seems to be in part why he is associated with agriculture.
9) Lug is a young champion: In original depictions, Mars is likewise a young warrior. It is only in the Imperial period he begins to be depicted as an older father figure.
10) Lug is part of the triad of kings: Mars was also part of the original triad of Roman gods. In the triad, Lug is also by far the most associated with war.
11) Lug is associated with prophecy: In the archaic Roman religion, Mars is strongly associated with prophecy, especially augury (prophecy of bird-reading)
12) Lug is associated with the hound or wolf: Mars is also associated with the wolf
13) Lug is associated with the boar: Mars is in archaic context associated with the boar.
13) Lug is married to Bua (Victory) and Nas (Death), among others: Various iterations of Mars in Briton have him pared with the goddess Victoria. Victory and death are also the two outcomes of battle.
14) Lug is associated with anger and battle-rage: Mars, and his Greek counterpart Ares, is associated with anger as well.
However, there is reason to link Lug to Mercury, and it was certainly the case that he was sometimes thought of as Mercury. In Gaul this might have been more the case than in Britain, where the warring aspect was decreased depending on the location. Because he is linked to music, inspiration and skill, he is sometimes associated with Mercury. However, by the time of the Empire, the knowledge of the gods in Rome was not great, and it is a fact that in the present we may in fact know more about the archaic roman gods than the Romans themselves by the high Empire.
We should remember that Gwydion is a figure much more akin to Mercury than Lleu or Lug. Certainly the archaic Mars, or even Sancus, had much in common,