Safari is by Apple, who seems to have decided to deprecate and replace every open source component that relicenses as v3 (such as OpenSSL and bash); their chances of allowing their team to come into contact with this work would be particularly poor as a result, not to mention their competing HEIF product.
Firefox is by Mozilla, and the browser team ships code under MPL2 (afaik) which permits dual-licensing with GPL2 - but not, as far as I can work out personally, either variant of GPLv3; is MPL2 permissible to dual-license with LGPLv3, or would they be required not to implement an encoder due to incompatibility? (Mozilla seems invested in the AV1 codec, so it’s safe to assume they would be interested in a lossless frame encoder with higher efficiency than lossy options.)
Chromium seems to accept any mix of BSD, (L)GPLv2, and (L)GPLv3 at a brief glance at their codebase, which is quite surprising. (I wonder if shipping Chrome Browser knowingly includes libxz under the GPLv3 terms. If so, that ought to have certain useful outcomes for forcing their hand on Widevine.)
None of these questions would be of any relevance with a less restrictive license, whether BSD or CC-BY or even GPLv2.
The LGPL is hardly "restrictive". If you aren't modifying the code, and for a codec if you are I have questions, then you've nothing to worry about.
Regarding license compatibility, which actually existing browser are you worried about the licensing terms of?