Yes, but GIF is based on LZW, as the article you linked to says. LZW was derived from LZ78. They both IIRC use a dictionary coding approach with an explicit dictionary that is constructed during processing. Indices into the dictionary are used to encode repetitions.

PNG uses deflate, which is based on a combination of Huffman coding and LZSS, which is derived from LZ77. LZ77 encodes repetitions using back references into a sliding window. To my understanding, LZSS also uses a dictionary based approach, but only for finding such repetitions during encoding.

So this does not answer the question if LZ77 was patented or not.

The Wikipedia article about LZ77 does cite a patent (https://en.wikipedia.org/wiki/LZ77_and_LZ78#cite_note-3) and somebody in the talk page mentions that there's been a law suite (https://en.wikipedia.org/wiki/Talk:LZ77_and_LZ78#Patent_cont...). However, quickly scanning over the patent, it seems to discuss an improved algorithm based on LZ77, perhaps it relates to LZS? (Note: not LZSS from above; this is again is a different algorithm)

The LZS page mentions a law suite sounding similar to the one from the talk page, but contains no direct reference to the patent: https://en.wikipedia.org/wiki/Lempel%E2%80%93Ziv%E2%80%93Sta... It also states that the LZS patent was filed in 1993 and expired in 2007 (due to not paying their fees).