I was just playing around here and got a good solution
Create the snippet:

I created a generic function for this:
function SetLookupLaunchTooltip(fieldname, tooltip) {
if (!!!tooltip) {
tooltip = "{{ snippets['Default Lookup Launch Tooltip']}}";
}
var lookupLunchButton = $("#" + fieldname + "_entityname").next().find("button.launchentitylookup");
lookupLunchButton.attr("data-original-title", tooltip);
lookupLunchButton.attr("aria-label", tooltip);
lookupLunchButton.find("span.sr-only").text(tooltip);
};
You can use it like this:
SetLookupLaunchTooltip("cr285_customerlookup");
// or
SetLookupLaunchTooltip("cr285_customerlookup","hello world");

If you want, you can probably apply this to any lookup on the page by adding the code to the Tracking Code snippet.