The goal is to get people to self-censor, including both people at home and expatriates. This is a common behavior of totalitarian regimes such as China's. It's well documented, for example, that the Chinese government works through agents to discourage Chinese students in the US from speaking against the regime. They want to make those people fear harm to themselves or their families, so that they will shut up.
Protasevich is simply a case where the methods were more shameless and overt.
It's quite sure that arresting him won't change anything, someone else will overtake his tasks.
I wish I could believe this. People as energetic, competent, honest, and altruistic as Protasevich are in short supply. Lukashenko's action against him is likely to be extremely effective in forcing other expat dissidents to self-censor.
An attack like this is also extremely attractive because there is no down-side. Lukashenko and Putin have been carrying out these attacks on people like Litvinenko and Protasevich with total impunity. Sanctions worked, for example, against apartheid-era South Africa, but they worked because they had an impact on people who were able to vote. If sanctions are imposed on Belarus, the people affected by them will not be able to do anything about it, because there are only sham elections. There is also a nuclear umbrella over Belarus and Russia, which makes their rulers feel impervious to threats against their regimes.