Lapland is a huge tract of land that expands on the territories of several countries. You might need to be a bit more specific on your place of departure.
Do you want to dodge tourists in their cars or ride endless empty gravel roads?
The farthest you could get by train is Kemijärvi. If you’d like to see and enjoy endless roads, nice scenery, good food, wilderness and historic places you could ride relatively close to the border all the way down to Joensuu and take a train back to Helsinki. If I had the time and company I would plan on riding thru something like:
Kemijärvi
Salla
Kursu
Kelloselkä
Aatsinki
Kallunki
Oulanka
Kuusamo
Murtovaara
Suomussalmi kk
Raate
Lentiira
Kuhmo
Nurmes
Joensuu
Imatra
Lappeenranta
Hamina
Porvoo
Helsinki
Places where you could take a train: From Kuusamo take a bus to Oulu where there are good connections. After Kuhmo you could ride towards Kajaani to take a train to Helsinki. Next possibilities are in Joensuu, Imatra and Lappeenranta.
Other people might disagree with my route suggestions.
In general - try to avoid roads with single digit numbers (1…9), also especially in the South even the two-digit-roads (10…99) can be pretty busy - and focus on three-digit-numbers (123 etc), they’re usually paved and carry you through more interesting scenery. usually. Even the 4-digits may be paved, but be ready to check it from Google Streetview or similar- just in case. In North the distances between i.e. shops/gas stations might be longish, in central/southern it should not be a problem.
Two digit roads can be pretty hazardous in Lapland aswell. I drive daily 100+ km on the kantatie 79 / kittiläntie (by car) and let’s just say I have little to no intentions of riding that road by bike (at least past certain point). The space for cyclists on the edge of the road is miniscule and the cars go by 100+ km/h on roads which might be filled with potholes that will brake the car or your bike.
Depending on the road there might be loads of big trucks, which makes it much more sketchy.
In certain areas the gravel roads are getting destroyed by melting snow, water and big trucks so if you are planning to ride those, first check if those roads are going to be under maintenance this summer. It’s called kelirikko and it’s pretty bad this spring.