You're probably thinking, "Take Lauren, create the nickname Laurie, change the spelling to Lori, then make a full name out of that nickname and you get Loria." Really, though, it is the elaborate Latin version of Lora, which came as a pet name for Eleanor in Italian, and also a short form of Dolores in Spanish. Whichever you prefer, Eleanor means "sun, bright," and Dolores "pain, sorrow." In modern times, however, Loria came about in English as a frilly version of Laura, which means "laurel" in Latin.
Although this is a rare name, it has been used since at least 1907 and it ranked in 1961 and 1962, the height of its popularity overall. However, it should be noted that it was only given to 132 girls in 1961 - the population was smaller so it took less to make it on the top 1000. In 2009 it was given to a mere 5 girls, and we haven't seen it since. Loriana, however, was given to 17 girls in 2016, and Lorianna to 7. It might be brought off the endangered list due to recent pop-culture use: this is a kingdom name in the fictional world of Fillory, which comes from The Magicians by Lev Grossman. His 2009 book was recently made into a TV series of the same name.
Loria is a place name as well, located in Veneto, Italy. The name most likely derives from the ancient Roman city Laurentum. There are also a few birds with Loria in their species name - these were named after ethnographer Lamberto Loria.
As a bonus, Loria can have the nickname Lore instead of Lori/Lorie. The definition of Lore is "a particular body of knowledge or tradition" according to Merriam-Webster. Mostly people associate the word lore with legends and oral tales. If Laurel (365 girls in 2015 and #772), Laura (1003 girls in 2015 and #322), Lorelei (700 girls in 2015 and #448 with the spelling Lorelai #651) or Lauren (2677 girls in 2015 and #119) are names that appeal to you, but you dread their eternal popularity, consider Loria. The spelling Lauria started being used around 1915, but it stopped being used in 1992. There are plenty of other variants and spellings of these names, including Laure, Loriana, Lauralei, Lorelie, Laureline, and Loralea.