This pertains to Ubuntu 12.04 LTS.
When PHP 5.3 goes end-of-life later this year, will Ubuntu 12.04 continue with PHP 5.3 (with backported security fixes?) or will there be a move to PHP 5.4?
This section answers the general question regarding software in the LTS release and what happens after EOL. This applies to most any software in the release.
12.04 LTS is a long term supported release, for up to 5 years for server. This does not mean that the specific versions of software included in 12.04 will continue to exist afterwards in later releases.
After 12.04 reaches End of Life, there is absolutely no guarantee that the versions of any given software in 12.04 will exist or be supported in later releases. It is very likely that the software that you will want will already have been version bumped to later releases, depending on the version in Debian at the time of the later release of Ubuntu being made.
During the lifespan of the LTS, however, the versions of the software in the LTS release are likely to stay the same, given the restrictions for version bumps in releases of Ubuntu.
This section answers the original question about PHP 5.3 and whether it'll be supported after 12.04 EOLs.
As long as 12.04 is not End of Life, it'll have PHP 5.3.
However, as 12.10 (Quantal) and later all have PHP 5.4.x or newer, and everything else after will have that depending on what is in Debian and what PHP upstream has released, after 12.04, there is no PHP 5.3 available in the repositories, however it might be available in a PPA. And that will likely be riddled with security bugs that are not fixed by the time 12.04 EOLs.
If you were too lazy to read all that, the answer to your question is, "No, there's no guarantee that PHP 5.3 will be available after 12.04's End of Life". It will be VERY likely that by the time 12.04 EOLs, not even PHP upstream will support 5.3.x anymore, and we might be on PHP 5.5.x as stable and PHP 5.4.x as legacy.