After researching more about this claim, my findings suggest that we cannot confidently say that this is true at all. When examining actual studies on lymphoma vs. tattoos, there are only two that have been conducted on this subject. The first study, listed here
https://pubmed.ncbi.nlm.nih.gov/32699076/, compared 1,518 people with lymphoma to those who don't, and found no correlation between the two at all. The second study, listed here
https://pubmed.ncbi.nlm.nih.gov/38827888/, is the one that people will reference for this claim or misinterpret. In this study, with a population of 11,905 people, they had 1,398 people with lymphoma and 4,193 people without. The results of this study found that 21% of people with lymphoma had tattoo(s), while only 18% of people in the control group had tattoo(s). The study shows a 3% higher chance of having lymphoma with tattoos. However, this number is not large enough to be considered statistically significant, nor has it been studied or looked into any further. It is a large stretch to jump to conclusions based on that study alone. Correlation does not always mean causation. According to Harvard Health Publishing
https://www.health.harvard.edu/blog/do-tattoos-cause-lymphoma-202407193059, the connection made between lymphoma and tattoos could have been made by chance. This article brings up the point that if they are truly connected, we would be seeing an increased number of people with lymphoma along with the increased popularity of tattoos, which is not what is happening at all. Additionally, there are no known official "causes" of lymphoma
https://www.mayoclinic.org/diseases-conditions/lymphoma/symptoms-causes/syc-20352638. There are risk factors, such as a family history of lymphoma or an autoimmune condition, but no evidence of any direct cause, as some articles may convey. Overall, there is not enough evidence or studies done to say that tattoos actually increase one's risk of lymphoma.