Segregating lab network from production at work.

Work has allowed me to set up a CCNA/CCNP lab on prem and I want to know the best way to segregate it while also getting internet access.

There are 2 routers and 2 switches currently in the configuration. If I come off of my core switch to one of the routers do I need VLANs at all since it will in theory be routed traffic and I can set a DHCP server on the router to feed the network below it? Also is there something I'm missing that I need to know to make sure that the DHCP on the router doesn't feed the other devices? Being on a different network they shouldn't see it right?

Edit: Should I be going to my ASA as the default route on the first router off of the core switch and then my first router as the default gateway for the second one?