Regarding lease vs purchase, it seems that monthly leases take 6 yrs and 9 months to reach the price that you would buy at. In terms of just lease price vs buy price, if you are planning on using a plane for more than 6.75 years, you should be buying it.
Growth should be considered when making the decision. An airline just starting likely won't be as well off with purchasing. It simply comes down to a purchase tying up more money today than some leases would. 6 planes leased for a year or 1 plane purchased... for expansion reasons (higher revenue from more planes running more routes), leasing might be your best option.
Company value should also be considered when making a decision. If you aren't in great need of expansion at the moment, buying could be a good choice for boosting company value and having more assets. Having higher company value and more assets means you should be able to get a bigger loan down the road when you are looking at getting a new hub or doing fleet replacement on old leases with new purchases.
Once you own a plane, you can use it and then have an option to sell it. If you have a lot of game time left, you could do something like purchase a plane, run it for 14 years to get over 200% of the use for the same money, and then sell it before it starts getting too old (or keep using it, you own it so it is your choice what you do with it).
With leases, if you are paying attention, you can lease planes around D-checks. Say there is a plane for sale with a D-check in 3.2 years. You could lease it for 3 years, then let it go and replace it with another lease (or a purchase at that time), avoiding having to pay a D-check that you would have needed to pay if you had purchased the plane.
I have also read a post or two about having a plane that you own being less expensive to maintain than a leased one, but I don't know for sure if that is the case. Someone else may be able to comment on that.
Now regarding your airline doing well but not earning very much, you should read up on some of the other threads to get some ideas about how to cut costs like maintaining a high level of fleet commonality and making your scheduling/routing more efficient to maximize both flight time and revenue.