People need to be aware of the invasive nature of certain garden plants and bamboo is one of them. You need to keep up the good work of pulling or digging it out and even using a weed killer, preferable a systemic one. I have nominated this for GoYopedia under invasive plants.

Sounds like an invasive one that needs attention asap.

Although this talks about the whole plant this RHS advice can be adapted for this growth.

The RHS say
"Invasive types of bamboo spread via long rhizomes, which help the plant to colonise new areas.

Chemical control
You can use a weedkiller to remove unwanted growth, or the whole plant. The larger the plant, the more difficult it will be to completely kill it, and it may take several applications of weedkiller to succeed
Eradicating unwanted growth

To ensure you only kill unwanted growth, first sever the underground rhizomes from the parent plant with a garden spade
Apply a tough formulation of glyphosate (e.g. Scotts Roundup Ultra 3000, Scotts Tumbleweed, Bayer Tough Rootkill, Bayer Super Strength Glyphosate or Doff Knockdown Maxi Strength Weedkiller) to the foliage of the section you want to kill
Consider replanting the original clump, or a division of it, inside a physical barrier to prevent future spread. See the bamboo profile for more information on physical barriers
Eradicating the whole plant

With very tall bamboos, which can be difficult to spray, cut down canes to soil level in late winter and then apply a glyphosate-based weedkiller (e.g. Scotts Roundup Ultra 3000, Scotts Tumbleweed, Bayer Tough Rootkill, Bayer Super Strength Glyphosate or Doff Knockdown Maxi Strength Weedkiller) to the young growth in late spring and early summer. Several treatments may be needed

Blimey Drc that took a lot of typing. Well done!

Let's not label all bamboos as invasive. Some, like pseudosasa japonica, can be thuggish, nay, invasive. However, many are perfectly well behaved (like our own Bamboo!) and are great garden plants in the right situation. Steady ye proponents of weedkillers and chemicals.

I agree Worthy and I have 2 that stay put and behave. But the questioners bamboo was removed by the previous owner and is still "coming up all over his lawn" This does not sound good to me.