Not positive, but i don't think so unless you are buying the house at the same time. If so, then i think you can spend it on what you want (or at least you'll have extra money with which to do it). Could be talking out my arrse though.
If the home improvements are for medical reasons then I believe there is an exception to this rule.
02.0414. Points to Note. Applicants should note that:
a. A LSAP for home extensions may be obtained only in the circumstances described in paragraph 02.0423.
b. No part of the LSAP may be used towards the cost of furnishings and fittings.
02.0423. Extenuating Medical/Family Circumstances. An applicant who would normally be disqualified from receiving a LSAP because they have owned a property within 50 miles of the chosen location, or within 50 miles of a current duty station or next duty station (as appropriate) during the 12 months preceding application (or, in the case of current duty station, at any time during the current assignment) may nonetheless qualify for a LSAP if able to demonstrate extenuating medical/family circumstances.
The applicant may apply for a LSAP either to purchase a new qualifying property, or to extend an existing property. In addition, the following conditions may apply:
a. Applicable Circumstances. One of the following medical/family circumstances must apply:
(1) Since the purchase of the current property, there is a specific medical requirement (defined as an existing condition which has deteriorated or a new medical condition) for more space than is available in the current property. Such an application must be supported by a medical certificate.
(2) In the case of personnel in PStat Cat 1 or 2, there are insufficient bedrooms for each child to have a separate one. A box room of 50 sq ft (4.75 sq m) or less may be disregarded in considering whether there are
sufficient bedrooms in a property; so may any larger box rooms in which it is impossible to fit windows. For the purpose of this scheme an unborn child(ren) expected to be born within 6 months is to be counted as a
member of the immediate family. The extenuating circumstances are:
(a) Additional dependant children since the purchase of the
current property; or
(b) Dependant children, at the time the property was purchased,
subsequently reaching the age of 11 years and over (only one
move every 2Â½ years within the same area is permitted).
(3) Since the purchase of the current property, there is a requirement
for an additional bedroom or space to accommodate, on a permanent
basis, an elderly or disabled relative. Any application must be supported
by a statement signed by the applicant to the effect that they are providing,
or about to provide, accommodation for an elderly or disabled relative on a
permanent basis. http://www.army.mod.uk/documents/general/jsp_752_version_7.pdf