Is it legal to sell flight tickets at a lower price than the airline's price?

All depends on the contract between the reseller and the airline. Without knowing the details about those contracts, it's impossible to say anything whatsoever.

And remember that the price a reseller pays to the airline is often considerably less than the price they charge you, the end user. That's their profit. So they're often quite capable of offering you a ticket at a price below the list price charged by the airline when dealing with you directly, without selling below the price they pay to the airline for the same ticket.

That's also why package holidays can often be offered at a price that seems impossible when you add up the prices of each individual part (air fare, bus fare, hotel price, meals), the tour operator buys in bulk, often far in advance, and gets a big discount on the list price.
Which can sometimes end up giving you, the customer, an added advantage. For example a few years ago an airline changed their schedule after my tour operator had bought the tickets, resulting in me getting to stay another night in a great beach resort on their expense because the flight home was now a day later.

But yes, it's quite possible for a reseller to sell you something below the list price of the item without running afoul of any contractual or legal obligations, just by buying low from their supplier.

In fact there is no direct contract between the airline and the travel agent (lastminute or other opaque booking site are also travel agents) regarding the price of flights.

Both have an agreement with a so-called GDS (Global Distribution System). It is not clear what exact terms of contract they use but overall a GDS connects with an airline to sell its flights and connects with a travel agent to distribute these flights.

In the contract with a GDS, you define the tools you want to access (as an airline or a travel agent), in particular the way to define the prices. For example the travel agent would want to access the opaque deals, some other good deals, or simply standard deals and it would cost a different price or some other conditions would differ.

I was unsure about the GDS handling also the opaque market but some article seems to confirm GDSes do.

So overall the price is not directly decided by the travel agent (even though they receive a fee on every booking and a possible extra fee that you pay at the end of your booking). It is the airline that actually offers a catalog of possible prices. And I cannot really imagine a travel agent selling a ticket for cheaper than it bought.

To add to it, this notion of "sale" (when items like clothes are sold for cheaper than the initial cost) comes from businesses that store the items they sell (so they have to get rid of all their items in the end). Travel agents do not "store" an amount of tickets.

Usually airlines and such companies have an agreement between each other.

The real cost of ticket is lower that price you buy at airlines. This difference is a profit of airline company. Airline company may give a right to sell tickets to other companies like Tui.com and so on. Tui may add some additional cost to real price of ticket.

But this additional cost may be lower than additional cost from airline company. Thats why tickets may be cheaper in Tui than in airline.