Streaming PS2 with a CRT

Hi! I recently bough an Elgato (the one with the RCA cables) in order to stream my PS2 with no need to convert it to HDMI manually. In the beggining I wanted to just play my favourites with no need to use my CRT. But I've heard the input lag directly via usb is horrible... So I'm considering just sending the signal via the elgato and just play it on the CRT. Is the Input lag that bad? If yes which cables would I need to make this work? Thank you.