A very odd itinerary indeed, since it is difficult to find flights from LGA to LHR, unless at least 1-stop.

After getting out of US and having landed in LHR, depending on the carrier, there may be a terminal transfer. That can be done airside or landside.

If going to landside (regardless of terminal transfer or not), there will be a passport control at the UK immigration. Then before catching the LHR-HEL flight (which depart from T3), there is a regular security check and screening of hand luggage, before entering the airside.

If doing the transfer using airside, a security check with screening of hand luggage takes place before entering the main terminal T3.

At HEL you will meet the much feared Finnish border guards (unless you have a Schengen e-passport and use the automatic booths) and passport check takes place. No screening for the hand luggage. 30 to 40 minutes should be ample time for change of plane, if the incoming flight is not delayed.

Customs is very active at HEL and most likely the ex-Schengen to Finland tagged luggage will be screened there. Finally at RVN you either contact the Customs or they may contact you, if necessary.