I know you said your db can handle it but still want to reiterate the point.
Are you sure your db can handle 1000 requests per second (assuming you want 1000 web req/s) in real-wolrd conditions? If it doesn't, it really doesn't matter what you choose as your script language as they are cpu bound where as dbs are hugely i/o.
If you have almost no db writes, then db is fine. But if you are using non-transaction safe db tables such as mysql's myisam tables then even a few writes per second will absolute destroy your performance goal due to table locks. Innodb would be ticket for mysql.
If LiteSpeed+PHP+LSAPI doesn't do it for you, use a app cluster setup and have it all conect to the same db, provied it can spawn/maintain 1000 active queries threads/processes. Or use a master/slave setup with the db and have each app machine host it's own sql environment so long read queries don't block the cluster performance.
If the queries are very redudant, data returned do not change often, use a middle tier cache such as memcached as lighting fast buffer for your db queries. If you can scale your db setup/data i/o fetch/write, you can scale everything else. With Lsws/PHP, you can always add more machines.