It depends on what kind of grass you have. But spray the correct weed-b-gone for your grass (read label) on the lawn to get rid of most broad-leaved weeds. Follow directions to the letter.

I have a thistle related to Canadian thistle. I've had total success cutting off the tap root below ground with a shovel. Dig it in at an angle from about 2 inches away from the root and cut it off. The plant does not come back.

As for the others, Yardvaark has the solution.

I get globe thistle. It laughed at Weed B Gon and RoundUp.

But it didn't laugh at Tenacity.

Yardvaark supplied the solution for the OP's most vexing problem?

We do like to chat.