Is the tree still alive? If it is, covering the roots with soil will do nothing but help to make the tree more vigorous and it will draw even more moisture from your lawn. If only some of the roots are in the lawn, you can chop them off near the tree. The roots then need to be physically removed. If the tree is dead, then you also need to remove the roots, as you will end up will toadstoools and fairy rings in your lawn.

Thank you

The tree is still alive, health and very tall, I think it is probably about 35 to 40 years old the roots are very thick. Do you think it would be safer to take it down?

It really depends on whether you want a decent lawn, to open up your garden to grow other plants or you need the privacy of the tree. If you do decide to take the tree down don't forget to take or have the stump ground out otherwise it may become a nuisance later.

I lean towards making a feature of it. I say this because in a garden near here, with a similar problem, big gnarled roots of a large tree have become a sort of wooden 'rockery' where shallow pots of low growing alpines and miniature bulbs have been 'buried' under a layer of bark chippings (it needn't be bark) in a semi- circle among and between the exposed roots. The edge of the lawn has been well defined around this feature and to me, anyway, it looks really interesting.
Depends on how much of your lawn you would wish to give up, however.

Thank you so much for all your help. El

Normally, covering the roots with soil stands a good chance of killing the tree, particularly if there is any clay content to the foundation of the turf.

Thank you; there is some clay in the soil.