Lms43PD-05-CG Photodiode Troubleshooting
Assuming you fix the obvious problems with the circuit mentioned in comments, you will still have some difficulties.

Let's say you are coupling 10% of the light from your LED into your photodiode. There's no quantum efficiency spec on the photodiode, so just for giggles we'll assume it's 100%. Then the expected photocurrent is

$$\frac{ P_{src} \eta \lambda e}{hc}$$

where \$P_{src}\$ is the source power, \$\eta\$ is the transfer efficiency, \$e\$ is the fundamental charge, and \$\frac{hc}{\lambda}\$ is the photon energy at your operating wavelength. Plugging in numbers, I get,

$$\frac {(10 {\rm \mu W})(0.1)(1.6\times 10^{-19} {\rm C})}{(0.3 {\rm eV})(1.6\times 10^{-19}{\rm J/eV})}$$

or about 30 uA.

The dark current of your photodiode is specified as 8 - 25 mA. 

This means you have a signal to noise ratio of not much more than 0.001.

You will probably need to do some fairly careful design to make this system work. Consider these changes:


Increase your source power dramatically
Use a lock-in amplifier to separate your signal (10 kHz) from the background noise of your receiver
Use well-designed optics to optimize the optical coupling from the source to the receiver. Optics for 4 um wavelength will need to be chosen specifically for this wavelength.
Shield your receiver carefully from any background light
Cool your receiver to reduce dark current