Don't confuse alloying with reacting -- intermetallic compounds (where metals chemically bond with one another) are relative rarities, while alloys are very common. An alloy is nothing more or less than a solid solution of two or more metals; for instance, common plumbing solder (from before lead was banned for this purpose) was a solution of anywhere from 30 to 70 percent tin, in lead. It could be mixed below the melting point of lead, because the molten tin would dissolve the lead (like water dissolving sugar) -- but when the resulting solution is frozen, the two metals remain dissolved.
Since different substances are more or less soluble in others (just as table salt is much more soluble in water than lead chloride, or sugar is soluble in water but not in gasoline), different alloys will and won't work. One we discuss a lot here is zinc in lead; lead will only dissolve about 2% zinc by weight, and zinc about 1.8% lead, so mixing lead and zinc to make bullets isn't a very good plan (the two solutions aren't miscible; they'll separate like oil from water).
Just as with solubility in water vs. hydrocarbons, there are different solubility families in metals; lead, tin, antimony, bismuth, and arsenic (possibly one or two other close chemical relatives) are one family, miscible in virtually any proportion; copper, zinc, aluminum, and tin are another (I include tin in the second family as well as the first because tin and copper alloy well; I don't know if tin alloys with zinc or aluminum), and the two families don't intermix well. If there's tin in your lead, though, you might be able to get the tin to take up some copper, and of course lead will take up small traces of less soluble metals (like zinc, and probably copper).