Greetings Ken:
To be honest, your blue spruce is not killing your grass. Rather, your tree is either casting too much shade that inhibits photosynthesis of the grasses immediately beneath or adjacent to the crown radius of the tree, OR the continuous accumulation of dropped needles caused by needle senescence has caused a soil acidifying effect detrimental to the growth of grasses immediately adjacent to this tree.
Recommendations: pruning your blue spruce to allow more light penetration to your lawn (consult w/ a certified arborist), lime the soil to increase pH (always verify soil pH before adding fertilizers), or plant shade-tolerant cool season grasses adjacent to this particular tree.
Best of luck!
