Do you believe that Loki and Lóðurr from the creation myth are the same god? Why or why not?
Yes, I do believe that Loki, Loptr, and Lóðurr could be references to the same — if not different faces/aspects of the same deity.
(a) There’s the theory proposed by the scholar Ursula Dronke that Lóðurr is “a third name of Loki/Loptr”. Her argument rests upon the mention of Odin, Hœnir, and Loki as a trio of Norse deities/beings in a few late folkloric writings, including the Haustlöng, in the prologue to Reginsmál, and also in the Faroese ballad, Loka Táttur.
(b) As well, the kenning for Odin, Lóðurr’s friend appears to parallel another well-known kenning for Odin, Loptr’s friend – just as Loki is similarly referred to as Hœnir’s friend in the Haustlöng — which I believe further suggests their connection as a trio of deities/beings.
While many scholars may agree with this identification, I realize that it is not universally accepted. One argument that can be made against this argument is that Loki appears as a malevolent being later in Völuspá, which does seem to conflict with the image of Lóðurr as a “mighty and loving” figure.
Many scholars, including Jan de Vries and Georges Dumézil, have also identified Lóðurr as being the same deity as Loki.
(c) Scholar Haukur Þorgeirsson suggests that Loki and Lóðurr were different names for the same deity based on that Loki is referred to as Lóðurr in the rímur Lokrur.(1) Þorgeirsson argues that the writer of the rímur Lokrur may have had access to information about this identification from an earlier traditional extant tale or that perhaps the author had drawn that conclusion based on a possible comparative reference to the Prose Edda, as Snorri does not mention Lóðurr.
Since knowledge of the contents of the Poetic Edda could just as easily not have been accessible – or familiar – to every poet around 1400 AD when the rímur was written, still Þorgeirsson argues for the traditional identification, by pointing to Þrymlur where the same identification is made with Loki and Lóðurr. Again, Þorgeirsson mentions the possibility that the 14th- and 15th-century poets possessed written sources unknown to us, or the idea must have come from an unlikely source where the poets could have drawn a similar conclusion that Loki and Lóðurr are identical, but the sources of that (possibly oral) tradition remain presently unknown. He concludes that if Lóðurr was historically considered an independent deity from Loki, then a discussion of when and why Lóðurr became identified with Loki is an intriguing concept that deserves more exploration, and in his article (linked below), he discusses what he believes are several possibilities, based upon what is known about poetic and linguistic structures in the 14th and 15th century.
(d) Since the Prose Edda mentions the sons of Borr in the same context as Völuspá mentions Hœnir and Lóðurr, some scholars have reasoned that Lóðurr might be another name for either Vili or Vé. (Viktor Rydberg was an early proponent of this theory, even though it seems that he may have abandoned support of it later, as mentioned by Þorgeirsson in his article linked below .)
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(1) “Outside of the rímur, the name Lóðurr occurs in three Old Icelandic poems; Háleygjatal, Íslendingadrápa, and Völuspá. In each case, it indicates a figure associated with Óðinn, but scholars have been divided on exactly whom the name refers to. The theory which is most frequently defended – and most frequently attacked – is that the name refers to Loki.” from Haukur Þorgeirsson’s article, “Lokrur, Lóðurr, and Late Evidence” here (on Academia.com)