Do group four elements gain or lose electrons?

Usually they lose four electrons, but depending on what they react with, they can gain two electrons or lose less than four electrons. If they lose electrons the resulting ion is positive, if they gain electrons the ion is negative.

Group 4 .....

By "group 4" are you referring to the numbering by the IUPAC where the elements in group 4 are Ti, Zr and Hf, or are you referring to the carbon family?

Ti, Zr and Hf are transition metals and only form metal ions when acted upon by acids or when their salts dissolve in water. They could potentially form positively charged ions with charges up to +4. Sometimes there is confusion concerning the oxidation state of an element and the actual charge. Titanium and its group 4 ilk commonly form compounds with oxidation states of +4, but not with actual charges of +4. There is a difference in the oxidation state and the electric charge on an atom in a compound.

The carbon family (C, Si, Ge, Sn and Pb) run the range from nonmetal, through metalloid to poor-metal. None of these form so-called "ionic" compounds. When they bond with other elements, the bonds are predominately covalent. So no, they don't form ions at all. Even PbO is covalent. Electrons are "shared", so to speak, but there are no transfers of electrons except in the case of some soluble salts of tin and lead as they dissolve in water:

.... SnCl2(s) --> Sn2+(aq) + 2Cl-(aq) ............. very dilute solution

.... SnCl2(s) + H2O --> Sn(OH)Cl(s) + HCl(aq) ...... hydrolysis

.... Pb(NO3)2(s) --> Pb2+(aq) + 2NO3^-(aq)

What you are really thinking about is whether the carbon family of elements exhibit oxidation numbers which are positive or negative. And the answer is yes. Carbon has oxidation states of +4 to -4, as does silicon and germanium. Tin and lead have oxidation states of +2 and +4. But please do not equate these oxidation states to ionic charges.