たまに bashスクリプトを書くと declare -l local_var って書いてしまって結局 man bash するのでいっそQiitaに書いておこうと思った始末。 (>= bash 4)
この場合の正解は local 
local [option] [name[=value] ...]
For each argument, a local variable named name is created, and assigned value. The option can be any of the options accepted by declare. When local is used within a function, it causes the variable name to have a visible scope restricted to that function and its children. With no operands, local writes a list of local variables to the standard output. It is an error to use local when not within a function. The return status is 0 unless local is used outside a function, an invalid name is supplied, or name is a readonly variable.
declare [-aAfFilrtux] [-p] [name[=value] ...]
Declare variables and/or give them attributes. If no names are given then display the values of variables. The -p option will display the attributes and values of each name. When -p is used with name arguments, additional options are ignored. When -p is supplied without name arguments, it will display the attributes and values of all variables having the attributes specified by the additional options. If no other options are supplied with -p, declare will display the attributes and values of all shell variables. The -f option will restrict the display to shell functions. The -F option inhibits the display of function definitions; only the function name and attributes are printed. If the extdebug shell option is enabled using shopt, the source file name and line number where the function is defined are displayed as well. The -F option implies -f. The following options can be used to restrict output to variables with the specified attribute or to give variables attributes:
declare -l
-l
When the variable is assigned a value, all upper-case characters are converted to lower-case. The upper-case attribute is disabled.