We should admit that the Litecommerce software is going to be slow as soon as you have got a few hundreds of the products. I think it is not a point to be limited so or use the slow software, so we should look what is possible to make here.
Firstly we should understand why it is so slow. As you know the litecommerce is based on the objects and each product/cart item/order/etc is such object. As the result when you try to find 100 products, the system is creating 100 objects of the product. In the Litecommerce is mean that at least 100 queries will be done to the database, because each row (each product) is selected separately. The amount of the queries will be increased greatly if some additional data is required for these products, for example thumbnails will add an additional 100 queries and so on. The amount of the queries is big factor for the mysql server performance, it can be floated by queries or, much simple, when you summarize the time of each query - you will receive a few seconds. If we are talking about the additional data we should notice the second problem: we have to make the cycles to query such data.
What we need to fix the situation, it is special classes which will create the objects from one query results. Of course it is possible only in some of the cases, for example on the category page or during the search.
The pack is present below, it is replaced the standard classes on the improved ones.