Holly,
On the Armed Forces World War One part of Rootschat there are people there with a lot more knowledge than me about these matters and you might want to record your enquiry there.
The Royal Inniskilling Fusiliers Museum does offer a "trace a relative" option online. You will note though that if you input the surname Lawrence that it brings up several William Lawrences. It may be a touch expensive at £65 per individual to make enquiries and have them send you the details about all the Private William Lawrences? The experts in the Armed Forces section may offer a less expensive alternative. Brown1777
