We need to lead by example where possible, but if you have a lazy DH then you need to demonstrate to your DC that this behaviour is not acceptable, both DDs and DSs.
DH is the best cook and will spend many happy hours in the kitchen. He also quite capable of cleaning up after himself and doing the food shopping.
We do tend to split jobs, so I am mainly responsible for cleaning and laundry, but DH will pitch in. He does tend to ask what load to put on re laundry, but that is because he knows I have a sort of system, but if he notices the ironing pile is growing he will do some, without complaint.
He has also been very involved with childcare, probably did more nappies than me, mainly because he is not squeamish and doesn't have a sense of smell. Which also helps with sickness and scrapes.
Both sets of parents were surprised by how much DH was involved with housework and then childcare when DS arrived on the scene, as they were very much of the opinion that there was man's work and woman's work (although MIL had taught DH how to cook before he went to university). But they learnt to accept what we did, and my DM has admitted to me that she wished my DF had been more involved.
Hopefully, this has given a good example to DS. DS is also responsible for putting his dirty laundry in the wash basket and put away his clean clothes. He also helps in the kitchen.
I would be ashamed of DS if he expects any future partner to do all the housework/childcare etc.
I would hope that society nowadays does not expect him to become a manchild.