Are there any flights from Luton Airport to Turku/Finland?

On Google Flights you can ask it to find routes from LTN to "Finland" and it will map possible destinations in the "Explore Destinations" panel, but it won't provide a list, just a map.

You can also go to the airport's Wikipedia page to find a list of its destinations and the airlines flying the routes; they're grouped by airline, not country, though.

I have just checked Skyscanner, and it accepts London Luton to Finland and gives a list of results with number of required stopovers. In this case each result in the month I used needs one stop. So it does not find direct flights.

A search on Kayak did find direct flights either. On that site you are restricted to 4 airports per country but it allows you to check on 'near' airports, and that near is not really near, covering a good part of Finland in one go.

Those are just two flight ticket sites, but if you search for air tickets or flights and your destinations you will likely find some more. Not all ticket sellers sites are as reliable, but you do not need to buy from the search sites.

There might be direct flights in some times of the year, I did check for some random dates/months. And there might be charter companies that have options to join their flights, which will not show up on a search like this as far as I know.

On all ticket sites I have ever used you can specify two airports to travel between, most or all also do 'all airports for a city' like all London airports, or all airports within a given radius from the one you select.

Also do many of the ticket search sites the option to chose just one day, or a longer period of time, some allowing up to a year to find the cheapest options between two airports.
The more options you have open, the less details you get for the results, but the options allow you do to a second search later which is more focused.

There are (practically speaking) no direct flights from Luton to Finland.

The destination map on the airport website does include Ivalo and Enontekiö, both in Arctic Finland. However, if you click the corresponding "schedules" links, you see that these are one-off charter flights on the 5th and 20th of December, respectively, presumably to see Santa Claus in Lapland. Note that Ivalo and Enontekiö are both a very long way from Turku: about 12–13 hours' drive, according to Google maps.