The direct reaction between the two elements are probably too violent and crude, so I would suggest that you slowly dissolve your lithium in methanol to form Lithium methoxide, and when it has all reacted and the solution cooled down, you add an equimolar amount of hydriodic acid solution (can be made from I2, see my page) dropwise to get a solution of lithium iodide.
Then the solvents are evaporated under vacuum in a flask situated in a boiling water bath to give crude lithium iodide. The lithium iodide is then recrystallized from boiling acetone (or from boiling water, using 0.5ml per gram LiI, followed by cooling in a freezer, preferably below -20°C to precipitate it all), filtered, and dried in a vacuum desiccator over phosphorous pentoxide for 1h at 60°C followed by 1h at 120°C (lithium iodide is extremely hygroscopic, so it must be rigorously dried to remove all the water).
Methanol is used to dissolve the lithium, because the reaction between lithium and water is too violent. The purification procedure is from a textbook, I don't know how much it can be simplified and still get a usable product. H2SO4 may substitute for the P2O5, and maybe the vacuum can be omitted, but I believe the dessiccator (or a ghetto version thereof) is a must. Could anyone comment on this idea?