The weed pictured here is Canada thistle (Cirsium arvense). Canada thistle is a creeping perennial. Most other thistles such as bull thistle are biennials, meaning they spend one year as a rosette and then send up a shoot with flowers in the second year. Canada thistle has lobed leaves with smooth upper surfaces and sharp-tipped spines on the margins. Bull thistle, in contrast, has rough hairs on the upper leaf surface.  

Canada thistle can keep returning from a large underground root system once the plant is pulled or dug. The best option to rid your lawn of this weed is the use of the herbicide triclopyr. This is the active ingredient in Bioadvanced Brush Killer Plus (recently renamed from Bayer Advanced Brush Killer Plus, you may see either). There may also be other products available, just be sure that the only active ingredient is triclopyr to avoid injuring your lawn. Applications made in the late summer to early fall (end of August through early October) are usually the most effective as perennials are moving carbohydrates to the root and rhizome system during that time and the herbicide will be more effectively translocated to that region then. Multiple applications may be necessary to rid your lawn of this perennial. As with any herbicide application, it is important to read and follow all labeled instructions.