EAGLE tool to LTSpice
Give up any thought that this would ever work in any sort of native way. LTSpice has its own built in schematic and symbol editors. Its behavioral models for components follow basic Spice compatible standards. 

Now if you fully 100% grokked the schematic and symbol file formats that come out of your CAD package and if you likewise fully understood the schematic and symbol file formats of LTSpice then it may be possible to write a translator to convert from your CAD to LTSpice. Estimating whether this is feasible cannot be made unless the relationships are understood however. (There is a reason that there is a healthy business environment for folks that provide such translators between various CAD packages).