Sir get the financing done by an Islamic bank, preferably from Dubai Islamic Bank or Bank Islami and not on variable rate.
Set the tenure to 5 years, you can also set the tenure lower to 3 or even 1 year to reduce the interest/profit paid to bank, but installment amount will increase considerably.
Pay as much equity as you can.
They will check your other loan obligations and makes a debt burden or debt/income ratio, i.e if your salary (take home) is 100,000, your calculated monthly installment cannot exceed 40,000, 60/40 ratio.
Bank will also check the period of service with your current employment and your credit history, if any or if you are businessmen, your business, income and assets.
You can only lease a car of 2005 August or later (if you will apply in August), if you will avail the financing of 550,000 and pay 300,000 cash as your equity for the total cost of 850,000 for Vitz, your average monthly installment will be 15,000 and you must show an income of 40-50K Rs take home with stable financial statements.
Takafaul/Insurance costs are 3% separate and tracker fee is around 1,500 Rs which is necessary for all imported/expensive cars.
You can also pay the principal (financing amount) early to avoid paying installment and interest.
I do not think you should buy an imported car on lease and make a switch from Alto to Vitz, I suggest you to buy a Late 2005 City Vario or Civic, if you can afford one.
Previously leased a 2005 Gli from meezan bank (paid early) and 2003 VTI ORIEL UG.