lob indexes and lob columns  should be in the same tablespace.
so you have to move the lob column (lob data) NOT the index

a lob data ( table) and lob index should be in the same tablespace.
YOU CANNOT MOVE JUST A LOB-INDEX or REBUILD THE LOB INDEX.

----------------------------------------------------------------------

dbadmin@mutation_mutation > create table test (c1 blob);

Table created.

dbadmin@mutation_mutation > select table_name,tablespace_name from user_tables where table_name='TEST';

TABLE_NAME                     TABLESPACE_NAME
------------------------------ ------------------------------
TEST                           USERS

dbadmin@mutation_mutation > select index_name,tablespace_name from user_indexes where table_name='TEST';

INDEX_NAME                     TABLESPACE_NAME
------------------------------ ------------------------------
SYS_IL0000007051C00001$$       USERS

-- this will fail

dbadmin@mutation_mutation > alter index SYS_IL0000007051C00001$$ rebuild tablespace tools;
alter index SYS_IL0000007051C00001$$ rebuild tablespace tools
*
ERROR at line 1:
ORA-02327: cannot create index on expression with datatype LOB

-- Will not work even for the same tablesapce 
dbadmin@mutation_mutation >  alter index SYS_IL0000007051C00001$$ rebuild tablespace USERS;
 alter index SYS_IL0000007051C00001$$ rebuild tablespace USERS
*
ERROR at line 1:
ORA-02327: cannot create index on expression with datatype LOB

-- i am moving the table with lob data from USERS to TOOLS tablespace
dbadmin@mutation_mutation > create table test (c1 blob);

Table created.

dbadmin@mutation_mutation > select tablespace_name,table_name from user_tables
  2  where table_name='TEST';

TABLESPACE_NAME                TABLE_NAME
------------------------------ ------------------------------
USERS                          TEST

dbadmin@mutation_mutation > select tablespace_name,index_name from user_indexes
  2  where table_name='TEST';

TABLESPACE_NAME                INDEX_NAME
------------------------------ ------------------------------
USERS                          SYS_IL0000007055C00001$$

"afiedt.buf" 3 lines, 87 characters

  1  alter table test move tablespace tools
  2* lob(c1) store as logsegment (tablespace tools)
dbadmin@mutation_mutation > /

Table altered.

"afiedt.buf" 2 lines, 80 characters

  1   select tablespace_name,table_name from user_tables
  2*     where table_name='TEST'
dbadmin@mutation_mutation > /

TABLESPACE_NAME                TABLE_NAME
------------------------------ ------------------------------
TOOLS                          TEST

dbadmin@mutation_mutation > select tablespace_name,index_name from user_indexes
  2   where table_name='TEST';

TABLESPACE_NAME                INDEX_NAME
------------------------------ ------------------------------
TOOLS                          SYS_IL0000007055C00001$$

it is upto u~.
lobs are just pointers!