You are mixing jQuery and native JavaScript. Either stick to document.get...... or use jQuery selector.
In your problem you can do that by using both ways
1) JavaScript way:
var other = document.getElementById("<%=lblother.ClientID %>").value;
document.getElementById("<%=txtother.ClientID %>").value = other;
2) jQuery way:
var other = $("#lblotherClientID").val();
$("#txtotherClientID").val(other);
This is not a rule. Infact it can be done as long as you know what your code is doing, but it is a good practice.