No, TIFF can be either Lossy OR Lossless. The format has options for both. As for GIF, GIF is actually lossless. The problem is that it only supports 256 colors. PNG is also lossless, and is generally a better replacement for GIF in most cases, and it supports multiple color depth options from 8-bit palletted up to very high truecolor (24/48-bit).
On the lossy side of things, it's really amazing how well old JPEG has held up all these years. However, for very high res photos, if you have good software, JPEG XR outstrips JPEG in quality.