Have to put my correcting hat on here
The walkthrough at Cotswold only has 3 species of Lemur with full access to what is a small enclosure. These are Crowned Lemur, Ring Tailed and Red Bellied.
The Greater Bamboo Lemur are elsewhere in the Walled Garden as are the Sifaka. The Belted Black & White Lemur, whilst in the walkthrough have no access to the walkthrough section and are confined to their own exhibit, as they have been known to attack the other Lemurs, so Cotswold only have 3 actual Lemurs in the walkthrough.
South Lakes Safari, also have 6 species of Lemur, 4 with access to the Walkthrough. Belted and Ruffled Black & White Lemur, Red Ruffled Lemurs, Ring Tailed Lemurs, White Fronted Brown Lemur, and a Hybrid cross between a White Fronted & Mongoose Lemur.
Then you can consider Woburn which also has 4 Lemur Species with access to the walkthrough, with Red Fronted, Red Bellied, Black & White Ruffled and Ring Tail.
Another exhibit with 4 in the walkthrough is Marwell, where they have Gentle Lemurs, Black & White Ruffled, Crowned & Ring Tail.
As well as Chester the Walkthrough's at Drusilla's hold Ring Tailed Lemurs & Black Lemurs.
Blackpool have three species in their walkthrough, and also have the Dwarf Mouse Lemur in the Monkey House.
However the award for the most Species of Lemur in a Walkthrough Exhibit goes to the Wild Place Project in Bristol. In the first walkthrough exhibit you will find Ring Tailed, Red Bellied and Mongoose Lemur, whilst in the second exhibit you will find Gentle (They aren't allowed access to the walkthrough section at the same time as the White & Black Belted Lemur's so they have an alternative outdoor as well) and White & Black Belted Lemur. This means you can get up close to 5 species of Lemur, the most in any walkthrough.
So with only 3 species of Lemur in it's walkthrough, Cotswold is already behind, South Lakes, Woburn, Marwell and Wild Place which all have 4 or more, meaning Cotswold are not on top when it comes to Walkthrough's but in holding 6 species they are still joint top with South Lakes albeit one of South Lake's is a hybrid.
This is only the places I've been to, so there could be a walk through with more than 5 somewhere I'm yet to come across.