#"H"_2"S"# is a weak acid.
#"H"_2"O:" + "H"_2"S" ⇌ "H"_3"O"^+ + "SH"^-#
#"H"_2"S"# is a Brønsted acid, because it is donating a proton to the water.
It is also a Lewis acid, because it is accepting a pair of electrons to form the #"O-H"# bond in hydronium ion.
#"H"_2"S"# has two lone pairs on the #"S"#, so it can also act as a Lewis base.
In the presence of a strong acid like #"H"_2"SO"_4#, the #"H"_2"S"# becomes protonated.
#"H"_2"S:" + "H"_2"SO"_4 → "H"_3"S"^+ + "HSO"_4^-#
Here the #"H"_2"S"# is donating an electron pair to form a bond to the #"H"# of #"H"_2"SO"_4#, so it is acting as a Lewis base.