Yes, Sri Lanka is capable of winning at home ground with the improvement in their performance and the way they are playing. However, it may not be so easy for Sri Lanka to win the match against New Zealand, because New Zealand is a very strong team. Since the Sri Lanka captain has decided to bat after winning the toss, then of course they know the pitch conditions here, which is why he has taken this decision. If Sri Lanka can chase a big target, then it will be easy to beat New Zealand, besides, Sri Lanka's current performance is very strong. However, we have seen that India was defeated by New Zealand at their home ground, so if Sri Lanka can perform strongly on such a ground, then New Zealand will be able to beat them. However, if such runs are made on today's pitch, then maybe New Zealand will have a chance to win because their bowling and batting are good.
Looking at New Zealand's XI, I am not at all optimistic about them. Against Sri Lanka's current performance, New Zealand's players will not be able to produce a good result. I bet New Zealand will not perform well given their position. Except for 2-3 players of ODI XI none of the players could play well in international cricket. None of them have the ability to perform in international cricket so far.
I am not criticizing the New Zealand team, just looking at their squad it is clear that winning the series is not their main goal. Their main goal in this series is to create new players. With a young team against an experienced team like Sri Lanka, New Zealand's match is more than difficult to win. Sri Lanka's current performance will also prove this sentence.