Do helium and lithium both give emission spectra?
Yes, they both give emission spectra.
All you have to do is supply enough energy from a flame or an electrical discharge to excite their electrons.
Below is a helium discharge tube being excited by a 5000 V transformer. Beside the image are the spectroscopic lines.
Here is the emission spectrum of lithium.
The red line is so intense that it is responsible for the colour when lithium salts are heated in a flame.