You can't do LLB through distance education. Although some universities do offer law degrees through distance education but they are not recognized by the Bar Council of India.
This means that you can not practice with such degrees since Bar Council of India does not recognize them. It also means that you won't be able to register with BCI.
The only option is to pursue LLB through regular mode. There are various universities in Punjab as well around the country that offers 3 years LLB course. You can apply for it despite having distance education graduation degree.
But since you are working, I don't think it would be possible to do job and study law at the same time. You will have to decide between work and LLB degree. Unless you have good job, there is no sense of doing LLB course. It would not be wise to quite a decent job.