My garen has two conifers at the edge of the lawn which has created a large area of dried out grass, what can I do to get the lushness of the lawn back?

I suggest getting rid of the conifers or the lawn is the only way as conifers will drain all the water and nutrients. I do not think you can have it lush and green.The huge amount of water you would need to apply every day (would go to the conifirs anyway.) even with regular feeding with greenup etc..
You could consider removing that part of the lawn and putting down bark instead. it would look good and be low maintainance. The bark, comes in dark or golden and I like the large decorative sort. I have only needed one top up in 10 years it is 4" deep and I rake it over twice a year.

More or less agree with Drc

Im stunned bamboo!

I have to agree with bamboo. I assume they are leylandii? If not, you could try feeding the grass, but this type of conifer will suck the life out of the soil and it is near on impossible to grow anything that requires nutrients in the soil below/surrounding the area. You could dig a bed around the base of the conifers, incorporate some organic matter - lots of it!! and plant some sedums, crocosmia and plants that will establish anywhere and don't need to be spoon fed!

Dunno why Drc - if the information is accurate, I'll agree, if its not, I won't, its as simple as that. Its all about the facts ...

Just so.