Can I travel outside of India if I have lost my expired passport but?
Yes, of course you can. I had a similar case. I had an expired passport which was never used. And thus after I renewed my passport I did not keep the old one safely. After sometime, when I was applying for visa, it asked for all the passports (current and expired) but I told them that I have never used my old passport and just gave them the number of old passport (this number will be present on your current passport) I was given the visa without any question asked about my old passport. And since then, I have travelled more than 15 countries without any issue.