Thank you for writing.
A lubricant itself should not cause a UTI unless there was bacteria transferred somehow. This should not happen in a clinical setting.
However, a small study found the vaginal exam itself could be a cause.
"We tried to determine whether women with a urinary tract infection (UTI) were more likely to have had a recent pelvic examination than were women seen for other reasons. We compared 56 women who were diagnosed as having a UTI with 49 controls who had an unrelated complaint (sinusitis). Significantly more women with UTIs had received a pelvic examination within the preceding 2 months (43% vs 16%, P = .01). We conclude that having a pelvic examination is associated with an increased risk of a UTI developing within the following 2 months. This may be due to physical factors related to the examination or to risk factors related to the patients' reasons for obtaining a pelvic examination. Further study is needed to determine if the pelvic examination is an independent risk factor. If so, established preventive measures could reduce this risk."
An interesting study, Anon, that could be the cause in your case. To read more, copy and paste this link : https://www.ncbi.nlm.nih.gov/pubmed/8640327