I do weight lifting once a week starting with a warm up set of 2kg, then sets of 14kg, and then drop sets. The last time I did was the 17th of October and after that my muscles were sore and now again lifting on the 30th of October I am sore again. I don't understand why my muscles are sore again. I tried to lift 16kg with a 2kg warm up as before and was barely able to do a 3rd rep at 16kg. I know DOMS happens when your body does a new effort of which it is not used to. After the DOMS goes away, does it mean that I have gained more strength than before and my body will adapt to the weight?
Between the 17th and 30th of October, almost two weeks have passed. That's far too long of a time period for your muscles to really get used to the movements and resistance.
If you want to avoid DOMS, and make better progress, you need to consider working out a lot more often. A good place to start is every 2 days.
After the DOMS goes away, does it mean that I have gained more strength than before and my body will adapt to the weight?
You might benefit from reading my response to a similar question. Although the question refers to a specific body part, the science behind my answer is still the same. To quote from that answer:
Current research indicates that there is no causal relationship to assume that DOMS/EIMD is a valid indicator for muscular progress (hypertrophy). As a result, I would suggest using a different indicator for your progress.