Lichen sclerosus affects the external skin. If you had internal only treatment, you weren't treated for lichen sclerosus unless the introitus was included as part of the inside and you were given local anesthesia. If you have an IC flare, see the physician who manages it for you and treat the flare with your regular meds.
Yes. Anything can cause a flare of IC. Hopefully, in the long run, treating your lichen sclerosis and vaginal atrophy will reduce total nociceptive windup and reduce your overall pelvic pain. I would treat any flare symptoms as you normally would and use Aquafor or similar petroleum products for the external areas.
I assume if you have LSA that the external genitalia were treated at level one power . This can cause 3-5 days of skin reaction (keep covered with vaseline, A+D, etc.). I also assume you do not have genital herpes as a cause of pain (medication needed). The IC symptoms require nothing to suddenly come on, and MLT could be an inciting cause. However, the benefits (off-label) of MLT are longer term, and down the line (anecdotal without study published yet). Just like with estrogen therapy, results are very unpredictable. IC is a difficult condition to promise results. Hopefully you will be better soon.