No, the few chemicals that would kill the vine foliage without killing the grass foliage would badly affect the rest of the vine. Usually, it's better just to keep your pruning shears handy.

Roots are another problem, Ehsanraya. Vine roots are rarely a problem in lawns. Are these large woody vines like Ivy or Wisteria?

yes it is (Variegated Ivy) and Ivy vines. It is the fence between my garden and the nieghbours gardens.

Ivy, aarrgghh! The only way to get rid of the roots is to dig them out, but first prune the Ivy back severely, removing up to 1/2 of the foliage, and don't disturb the roots within 50 cm of the wall. An edging at least 25 cm deep at that distance should reduce the chances of the roots coming up again farther out. Another thing that helps keep the roots down is to water deeply, but infrequently. If you must water the lawn, put at least 5 cm on at a time, but don't do that more often than once a month--I'm estimating from what I know about winter lawn needs here in the desert, and the climate in the UK, so you might want to check with Bamboo or Moon_Grower about that!