Its called Fibresure isn't it? I didn't take any fibre supplements while on LT and got mildly constipated first time I went to the toilet, all other times after that have been fine so that might have been a water thing.
The Fibresure stuff increases your fibre intake without any additional calories. It bulks up the waste in your gut so theres a mass for your intestines to push along. In basic terms your intestines sort of contract and relax to squeeze material along it, if theres more material because of fibre, your intestines keep pushing it along.
However, it is important to keep your water up because excess water is absorbed from what you eat in the large intestine, if you don't have enough water this will result in dry and hard stool ie constipation.
It really seems to vary from person to person as to whether you need to use the stuff or not, I didn't and haven't encountered any real problems or needed to use laxatives but others have done.
One thing to ask yourself is do you normally have any trouble passing motions and how regularly you go. If everything is fairly normal in that department then perhaps the fibre supplement isn't necessary and just watch your water intake. If you feel you do suffer from constipation at all or seem to have a very long digestive cycle then ask for the fibre supplement which the chemist should sell.
I don't know how LT safe it is but you can find similar supplements in Boots, one I currently use now that I've stopped LT is Benefibre. Dissolves in pretty much anything and two teaspoons gives me something like 70% of the fibre you need daily, does seem to make you pass wind more often but its completely odourless which is a good sign biologically speaking.