Those 2 big hoses are the oil lines from the motor going to and from the front oil coolers. It could be the fitting needs to be tightened just a bit more or the fitting to the hose is leaking. I would try tightnening the fitting up first. You really have to crank hard on it to get it tight so use the correct wrench and pull hard (not TOO hard and be careful). If that doesn't fix it you may have to replace the fitting and/or the hose. Check the other ends of the hoses up by the oil coolers too. Oil cooler on each side. You can see them from inside the front wheel wells through the grills. Nice and clean underneath! Check the oil level in the motor and keep it up to at least 1/2 way between the full and low marks. Check the power steering too. And the coolant level. The coolant header tank by the motor should always be full when cold and the overflow tank in the right rear wheel well should be at the cold line. Looks like the car was recently serviced by a Lotus dealer. If it was, take it back and let them tighten it up. They may have taken the hose off to drain out the oil when they changed the oil in the motor. Since you just bought the car it is VERY important to make sure all of the service is up to date.
Take a paper towel and run it around the base of the hose fitting and see if the oil is coming from the threads into the block, the swivel end, or the crimped hose fitting. Might need to dry the whole area , run then check, Isolating which spot is leaking is the first step.Hard to tell from the photos but it looks like the hose crimp band might be seeping. A hose shop might be able to crimp it a bit more, but it might need a new hose to fix. I'm hoping it's leaking at the swivel joint and could be tightened like Davis said