SQL Server: Lead/Lag analytic function across grou

Sorry for the long post, but I have provided copy & paste sample data and a possible solution approach below. The relevant part of the question is in the upper part of the post (above the horizontal rule).

I have the following table

 Dt          customer_id  buy_time     money_spent
 -------------------------------------------------
 2000-01-04  100          11:00:00.00  2
 2000-01-05  100          16:00:00.00  1
 2000-01-10  100          13:00:00.00  4
 2000-01-10  100          14:00:00.00  3
 2000-01-04  200          09:00:00.00  10
 2000-01-06  200          10:00:00.00  11
 2000-01-06  200          11:00:00.00  5
 2000-01-10  200          08:00:00.00  20

and want a query to get this result set

 Dt          Dt_next     customer_id  buy_time     money_spent
 -------------------------------------------------------------
 2000-01-04  2000-01-05  100          11:00:00.00  2
 2000-01-05  2000-01-10  100          16:00:00.00  1
 2000-01-10  NULL        100          13:00:00.00  4
 2000-01-10  NULL        100          14:00:00.00  3
 2000-01-04  2000-01-06  200          09:00:00.00  10
 2000-01-06  2000-01-10  200          10:00:00.00  11
 2000-01-06  2000-01-10  200          11:00:00.00  5
 2000-01-10  NULL        200          08:00:00.00  20

That is: I want for each costumer (customer_id) and each day (Dt) the next day the same customer has visited (Dt_next).

I have already one query that gives the latter result set (data and query enclosed below the horizontal rule). However, it involves a left outer join and two dense_rank aggregate functions. This approach seems a bit clumsy to me and I think that there should be a better solution. Any pointers to alternative solutions highly appreciated! Thank you!

BTW: I am using SQL Server 11 and the table has >>1m entries.

My query:

 select
   customer_table.Dt
   ,customer_table_lead.Dt as Dt_next
   ,customer_table.customer_id
   ,customer_table.buy_time
   ,customer_table.money_spent
 from
 (
   select 
     #customer_data.*
     ,dense_rank() over (partition by customer_id order by customer_id asc, Dt asc) as Dt_int
   from #customer_data
 ) as customer_table
 left outer join
 (
   select distinct
     #customer_data.Dt
     ,#customer_data.customer_id
     ,dense_rank() over (partition by customer_id order by customer_id asc, Dt asc)-1 as Dt_int
   from #customer_data
 ) as customer_table_lead
 on
 (
   customer_table.Dt_int=customer_table_lead.Dt_int
   and customer_table.customer_id=customer_table_lead.customer_id
 )

Sample data:

 create table #customer_data (
   Dt date not null,
   customer_id int not null,
   buy_time time(2) not null,
   money_spent float not null
 );

 insert into #customer_data values ('2000-01-04',100,'11:00:00',2);
 insert into #customer_data values ('2000-01-05',100,'16:00:00',1);
 insert into #customer_data values ('2000-01-10',100,'13:00:00',4);
 insert into #customer_data values ('2000-01-10',100,'14:00:00',3);

 insert into #customer_data values ('2000-01-04',200,'09:00:00',10);
 insert into #customer_data values ('2000-01-06',200,'10:00:00',11);
 insert into #customer_data values ('2000-01-06',200,'11:00:00',5);
 insert into #customer_data values ('2000-01-10',200,'08:00:00',20);

Try this query:

select cd.Dt
    , t.Dt_next
    , cd.customer_id
    , cd.buy_time
    , cd.money_spent
from (
    select Dt
        , LEAD(Dt) OVER (PARTITION BY customer_id ORDER BY Dt) AS Dt_next
        , customer_id
    from (
        select distinct Dt, customer_id
        from #customer_data
    ) t
) t
inner join #customer_data cd on t.customer_id = cd.customer_id and t.Dt = cd.Dt

Why field money_spent has float type? You may have problems with calculations. Convert it to decimal type.