I don't think that cartridge is a lip fire; I seem to see what looks like a pin driven all the way in. And the lip fire was not struck from the top but from the rear like any other rimfire cartridge. IMHO, it is a pinfire, though the cartridge is quite odd looking and may be a dummy of some kind.
The gun looks like one of many double barrel pistols made in Spain, and later in Brazil and other countries, often called a "garrucha". They were sold in areas where natives were not allowed to own repeating pistols, but could own double barrel pistols. They were made first as flintlocks, then percussion, then pin fire and finally conventional rimfire or center fire, in several calibers. Pictures of any proof marks would help in determining the country of origin.
The derringer seems to be a "Pointer" made by Hopkins and Allen c. 1870's to 1890 in .22 rimfire and .30 rimfire. Flayderman (8A-114) lists value at $225 for very good, but that gun does not come up to that level. I would guess at a value of around $100-125.
FWIW, the term "suicide special" was usually used for inexpensive revolvers, not single shot "derringers."