Oh dear. The good news is, its not poisonous (we don't have poison ivy in the UK). The bad news is, it looks like Convulvulus arvensis, one of the bindweeds, and they are difficult to eradicate, particularly in cultivated areas. Info in the link below

https://www.rhs.org.uk/advice/profile?PID=241

The usual procedure is to insert bamboo canes where it's growing, let it twine to the top, then spray with glyphosate, but that's not really an option when its growing in a lawn, too much risk of spray drift onto the grass, so probably all you can do is mow it, but be sure to collect up the clippings and don't allow flowers to form, to prevent seeding.

You can use the bamboo cane and glyphosate treatment if it grows in borders, but protect any surrounding plants from the spray. If you don't have glyphosate already, you might want to invest in a plentiful supply - it's likely to be withdrawn in the near future, and use glyphosate concentrate, mix it up yourself and use in a spray rather than buying Roundup.

You can get it in gel form where you can, if you have enough patience, paint it on the individual leaves.
Mowing regularly so that the leaves never get chance to photosynthesise will go a long way to discouraging it but its a long job.