2 things I think you need to consider here:
1. Precipitated withdrawal (p/d). Have you waited enough from your last of lortab to dose suboxone. The withdrawal needs to be medium to severe or enough time needs to pass, at least 24 hours to be safe. Some people can dose sub after just something like 8 hours, but some need to wait much longer. With something like lortab, which is a full agonist with a pretty short half life, I think 24 hours would be well enough of a wait.
2. How much suboxone to dose. You dont want to dose higher than you need because you will only be going backwards. Suboxone is itself a very potent opioid. You need to judge what your tolerance is. For someone who is stopping high dose methadone or high dose IV heroin, they might need 8mg or more. But for smaller habits you could probably dose 0.5mg or maybe even less. You can try like 1/5 of a mg and then wait an hour and see. If that helped then great. Dose lower next time. If not, dose higher. Sub is really really potent and works better at lower dosages anyways. Read this:
Suboxone induction
It's hard to dose that low with an 8mg pill. Personally, I dissolve sub in water to get the tiny amounts I use and then plug that amount. Works great, just as well as sublingual. I do this with the strips, can be done with pills or whatever form. Example:
8mg(sub)/40ml(water)=0.2mg of sub in every ml of water.
Then all you need is a 3-5 ml needle less syringe.