Hi Peanuts and welcome to GoY. The two images you have put up are of different plants and neither appears to be growing in grass! Given that you have just moved into the house I would suggest that you wait and see what the flowers on both of the plants look like and post images of them in flower.

The second picture looks like Symphoricarpos common name is Snowberry bush. We had it in the back of the house when we were in the farm it sends up suckers and was quite a mennace and hard to pull up. The roots run under ground quite wirelike and tough. Look it up on Google. If it is it will bear little white soft berries. The patch used to grow to about 4ft, quite a dence thornless hedge but a mennace to controle.

Both Symphoricarpus....the first picture shows the young suckers and the second shows the adult growth.

Tis the bane of my life and a swine to get rid of !!!!

Does glyphosate work? The lawn I the photo looks thin, if it was all sprayed off would that kill the suckers?

I have managed to kill off the row of it which was outside our front, but it has taken 2 years or regular spraying,every time a leaf appeared. Tough stuff!

Thank you so much for all of this advice. I'll wait to hear re the SBK advice. Is it the kind of thing I can dig out from the lawn, and should I try and cut it back at all ? I'm thinking each year its going to invade further into the garden. Great website by the way !

If all the lawn is like the photo I would kill the lot and start again once its clear. There doesn't look to be much grass anyway. You might have a season growing annuals there until you're sure its all gone, and then resow or turf in the autumn or next April. Not nice to lose your lawn for a year but probably worth it in the long run.

Thats what I wondered Stera,

Welcome to Goy Peanuts.......have a wander around the blogs and photo's if you've time