For LSIL results in a pap, an HPV positive co-test result is norm for the vast majority of cases, but not always. You'll have to spend some time googling why in order to satisfy your need to know (like if the other causes can be spread by intercourse), but, for now, just know that it is indeed possible to have the results you received. From what I understand, and please confirm this, you'll just have another pap in a years time to see what's going on.
Anyway, on to your other question... Having LSIL without HPV is indeed preferable. HPV isn't fun so if you don't have it, that's good. You don't say how old you are, but think forward to how many sexual partners you may yet have in life. Knowing that HPV is incredibly common, both warts and the cancer causing type, you're almost sure to get some type of it going forward especially if you don't use protection. If you're in a committed, long-term relationship, the fallout isn't too bad, but in the dating world, it can really be a blow to your self-esteem, and your way of thinking about your sex life and future. Better to avoid that route by using protection and choosing partners more cautiously. Unless a man hasn't had sex in three months, he has no way of really knowing whether he has warts or not because even with protection, he can get them on the scrotum or base of the penis not covered by the condom. After three months without any warts, it's safe to say he didn't get them from his last encounter. Also, the cancer causing strains have no symptoms in men so he can have the virus and never know it. That's why it spreads so easily. My gut feeling is that your LSIL cause is not a big deal and you can go forward normally in life. But now that you've had a chance to think about this topic, I'd educate myself if i were you and move forward with the determination not to do anything stupid sexually that you'll regret. It's not worth the aftermath, believe me.